Important Questions Class 10 Maths Chapter 2: Polynomials With Solutions

A polynomial is an algebraic expression made using constants, variables, and non-negative integer powers of variables. For example, x² + 7x + 10 is a quadratic polynomial, and its zeroes make the polynomial equal to zero.

A zero of a polynomial is the x-coordinate where its graph crosses or touches the x-axis. That geometric fact connects graph reading, factorisation, and coefficient relationships in Chapter 2. CBSE 2026 tests Important Questions Class 10 Maths Chapter 2 through zeroes from graphs, zeroes of quadratic polynomials, and relationships between zeroes and coefficients. The NCERT Reprint 2026-27 includes graph-based zeroes and zeroes-coefficients relationships. The Division Algorithm does not form part of the CBSE 2026 syllabus.

Key Takeaways

• Polynomials: Chapter 2 focuses on graphical zeroes, quadratic zeroes, and zeroes-coefficients relationships.
• Main Rule: Zeroes are the x-coordinates where the graph meets the x-axis.
• Exam Trap: In ax² + bx + c, the sum of zeroes is -b/a, not b/a.
• CBSE 2026 Update: Division Algorithm is not included in Class 10 Polynomials for CBSE 2026.

Important Questions Class 10 Maths Chapter 2 Structure 2026

Important Questions Class 10 Maths Chapter 2: Key Relationships

The relationship between zeroes and coefficients drives most algebra questions in this chapter. Write the formula first, then substitute values carefully.

Q1. What Is The Relationship Between Zeroes And Coefficients Class 10 For A Quadratic Polynomial?

For ax² + bx + c, the sum of zeroes is -b/a and the product of zeroes is c/a. These formulas apply when a ≠ 0.

1. Given Data:
   Polynomial = ax² + bx + c
   Zeroes = α and β
2. Formula Used:
   α + β = -b/a
   αβ = c/a
3. Final Result:
   Sum = -b/a and product = c/a

Q2. How Do You Form A Quadratic Polynomial From Sum And Product Of Zeroes?

A quadratic polynomial with given zeroes is x² - (sum of zeroes)x + product of zeroes. Any non-zero multiple has the same zeroes.

1. Given Data:
   Sum of zeroes = S
   Product of zeroes = P
2. Formula Used:
   Polynomial = x² - Sx + P
3. Final Result:
   Quadratic polynomial = x² - (sum)x + product

Q3. What Is The Relationship For Cubic Polynomial Class 10 Important Questions?

For ax³ + bx² + cx + d, use three zeroes α, β, and γ. The formulas connect their sum, pairwise product, and product to coefficients.

1. Given Data:
   Polynomial = ax³ + bx² + cx + d
   Zeroes = α, β, γ
2. Formula Used:
   α + β + γ = -b/a
   αβ + βγ + γα = c/a
   αβγ = -d/a
3. Final Result:
   Cubic zeroes follow three coefficient relationships

Q4. What Is The Geometrical Meaning Of Zeroes Class 10?

The zeroes of a polynomial are the x-coordinates where y = p(x) meets the x-axis. A polynomial of degree n has at most n zeroes.

1. Given Data:
   Graph of y = p(x)
2. Rule Used:
   Number of zeroes = Number of x-axis intersections
3. Final Result:
   Zeroes are x-axis intersection points

Polynomials Class 10 MCQ With Answers

These polynomials class 10 MCQ questions test graph reading, formula application, and degree identification. Each question follows the CBSE 2026 board exam pattern.

Q1. How Many Zeroes Does A Polynomial Have If Its Graph Intersects The X-Axis At Two Points?

The polynomial has 2 zeroes. Zeroes are the x-coordinates where the graph intersects the x-axis.

1. Given Data:
   Graph intersects the x-axis at two points.
2. Rule Used:
   Number of zeroes = Number of x-axis intersections
3. Final Result:
   Answer: (C) 2

Q2. If One Zero Of x² + 3x + k Is 2, Find k.

The value of k is -10. Substitute x = 2 because 2 is a zero.

1. Given Data:
   Polynomial = x² + 3x + k
   Zero = 2
2. Formula Used:
   p(2) = 0
3. Calculation:
   2² + 3(2) + k = 0
   4 + 6 + k = 0
   k = -10
4. Final Result:
   Answer: (A) -10

Q3. Find The Sum Of Zeroes Of 2x² - 8x + 6.

The sum of zeroes is 4. Use α + β = -b/a.

1. Given Data:
   a = 2
   b = -8
   c = 6
2. Formula Used:
   Sum of zeroes = -b/a
3. Calculation:
   Sum = -(-8)/2
   Sum = 8/2
   Sum = 4
4. Final Result:
   Answer: (A) 4

Q4. Find The Product Of Zeroes Of x² - 5x + 6.

The product of zeroes is 6. Use αβ = c/a.

1. Given Data:
   a = 1
   b = -5
   c = 6
2. Formula Used:
   Product of zeroes = c/a
3. Calculation:
   Product = 6/1
   Product = 6
4. Final Result:
   Answer: (C) 6

Q5. Find The Quadratic Polynomial With Zeroes -3 And 2.

The quadratic polynomial is x² + x - 6. Use sum and product of zeroes.

1. Given Data:
   Zeroes = -3 and 2
2. Formula Used:
   Polynomial = x² - (sum)x + product
3. Calculation:
   Sum = -3 + 2 = -1
   Product = (-3)(2) = -6
   Polynomial = x² - (-1)x + (-6)
4. Final Result:
   Answer: (A) x² + x - 6

Q6. If A Parabola Opens Upwards, What Is The Sign Of The Coefficient Of x²?

The coefficient of x² is positive. A parabola opens upwards when a > 0.

1. Given Data:
   Graph is a parabola opening upwards.
2. Rule Used:
   For y = ax² + bx + c, upward opening means a > 0.
3. Final Result:
   Answer: (C) Positive

Q7. If Zeroes Are Equal In Magnitude And Opposite In Sign, What Is The Coefficient Of x?

The coefficient of x is 0. Zeroes α and -α have sum 0.

1. Given Data:
   Zeroes = α and -α
2. Formula Used:
   Sum of zeroes = -b/a
3. Calculation:
   α + (-α) = 0
   -b/a = 0
   b = 0
4. Final Result:
   Answer: (A) 0

Q8. Find The Number Of Zeroes Of p(x) = (x - 3)² - 4.

The polynomial has 2 zeroes. Solving p(x) = 0 gives two values.

1. Given Data:
   p(x) = (x - 3)² - 4
2. Formula Used:
   p(x) = 0
3. Calculation:
   (x - 3)² - 4 = 0
   (x - 3)² = 4
   x - 3 = ±2
   x = 5 or x = 1
4. Final Result:
   Answer: (C) 2

Q9. If α And β Are Zeroes Of x² - 6x + 8, Find α² + β².

The value of α² + β² is 20. Use (α + β)² - 2αβ.

1. Given Data:
   Polynomial = x² - 6x + 8
2. Formula Used:
   α + β = -b/a
   αβ = c/a
   α² + β² = (α + β)² - 2αβ
3. Calculation:
   α + β = 6
   αβ = 8
   α² + β² = 6² - 2(8)
   α² + β² = 36 - 16
4. Final Result:
   Answer: (A) 20

Q10. Find The Zeroes Of x² - 3.

The zeroes are √3 and -√3. Solve x² - 3 = 0.

1. Given Data:
   Polynomial = x² - 3
2. Formula Used:
   p(x) = 0
3. Calculation:
   x² - 3 = 0
   x² = 3
   x = ±√3
4. Final Result:
   Answer: (A) ±√3

Geometrical Meaning Of Zeroes Class 10 Questions

These geometrical meaning of zeroes class 10 questions follow Section 2.2 of the current NCERT book. Count the points where the graph cuts or touches the x-axis.

Q1. How Many Zeroes Does A Polynomial Have If Its Graph Does Not Intersect The X-Axis?

The polynomial has no real zeroes. A real zero exists only where the graph meets the x-axis.

1. Given Data:
   Graph does not meet the x-axis.
2. Rule Used:
   Zeroes are x-coordinates of x-axis intersections.
3. Example:
   The graph of x² + 4 does not meet the x-axis.
4. Final Result:
   Number of real zeroes = 0

Q2. If The Graph Of y = p(x) Touches The X-Axis At One Point, How Many Zeroes Does It Have?

The polynomial has one repeated zero. The graph touches the x-axis at one x-coordinate.

1. Given Data:
   Graph touches the x-axis at one point.
2. Rule Used:
   Touching point gives a repeated zero.
3. Example:
   x² - 6x + 9 = (x - 3)²
   It touches the x-axis at x = 3.
4. Final Result:
   Number of distinct zeroes = 1

Q3. If A Cubic Polynomial Graph Cuts The X-Axis At Three Points, How Many Zeroes Does It Have?

The polynomial has three zeroes. Each x-axis intersection gives one real zero.

1. Given Data:
   Cubic graph cuts the x-axis at three distinct points.
2. Rule Used:
   Number of zeroes = Number of x-axis intersections
3. Final Result:
   Number of zeroes = 3

Q4. If A Parabola Opens Downwards And Intersects The X-Axis At Two Points, What Is The Sign Of a?

The value of a is negative. A parabola y = ax² + bx + c opens downwards when a < 0.

1. Given Data:
   Parabola opens downwards.
2. Rule Used:
   For y = ax² + bx + c, downward opening means a < 0.
3. Final Result:
   a is negative

Zeroes Of A Polynomial Class 10 Important Questions With Solutions

Finding zeroes by factorisation is one of the most tested skills in this chapter. These zeroes of a polynomial class 10 important questions cover factorisation and verification.

Q1. Find The Zeroes Of x² + 7x + 10 And Verify The Relationship.

The zeroes are -2 and -5. Their sum and product match the coefficient formulas.

1. Given Data:
   Polynomial = x² + 7x + 10
2. Formula Used:
   α + β = -b/a
   αβ = c/a
3. Calculation:
   x² + 7x + 10 = (x + 2)(x + 5)
   x = -2 or x = -5
4. Verification:
   Sum = -2 + (-5) = -7
   -b/a = -7/1 = -7
   Product = (-2)(-5) = 10
   c/a = 10/1 = 10
5. Final Result:
   Zeroes are -2 and -5

Q2. Find The Zeroes Of x² - 3 And Verify The Relationship.

The zeroes are √3 and -√3. Their sum is 0, and their product is -3.

1. Given Data:
   Polynomial = x² - 3
2. Formula Used:
   α + β = -b/a
   αβ = c/a
3. Calculation:
   x² - 3 = 0
   x² = 3
   x = √3 or x = -√3
4. Verification:
   Sum = √3 + (-√3) = 0
   -b/a = 0
   Product = (√3)(-√3) = -3
   c/a = -3
5. Final Result:
   Zeroes are √3 and -√3

Q3. Find The Zeroes Of x² - 2x - 8 And Verify.

The zeroes are 4 and -2. Their sum is 2, and their product is -8.

1. Given Data:
   Polynomial = x² - 2x - 8
2. Formula Used:
   α + β = -b/a
   αβ = c/a
3. Calculation:
   x² - 2x - 8 = (x - 4)(x + 2)
   x = 4 or x = -2
4. Verification:
   Sum = 4 + (-2) = 2
   -b/a = -(-2)/1 = 2
   Product = 4 × (-2) = -8
   c/a = -8
5. Final Result:
   Zeroes are 4 and -2

Q4. Find The Zeroes Of 4s² - 4s + 1 And Verify.

The zeroes are 1/2 and 1/2. This polynomial has repeated zeroes.

1. Given Data:
   Polynomial = 4s² - 4s + 1
2. Formula Used:
   α + β = -b/a
   αβ = c/a
3. Calculation:
   4s² - 4s + 1 = (2s - 1)²
   2s - 1 = 0
   s = 1/2
4. Verification:
   Sum = 1/2 + 1/2 = 1
   -b/a = -(-4)/4 = 1
   Product = (1/2)(1/2) = 1/4
   c/a = 1/4
5. Final Result:
   Zeroes are 1/2 and 1/2

Q5. Find The Zeroes Of 6x² - 3 - 7x And Verify.

The zeroes are -1/3 and 3/2. Rewrite the polynomial in standard form first.

1. Given Data:
   Polynomial = 6x² - 3 - 7x
2. Formula Used:
   α + β = -b/a
   αβ = c/a
3. Calculation:
   6x² - 3 - 7x = 6x² - 7x - 3
   6x² - 7x - 3 = (3x + 1)(2x - 3)
   x = -1/3 or x = 3/2
4. Verification:
   Sum = -1/3 + 3/2 = 7/6
   -b/a = -(-7)/6 = 7/6
   Product = (-1/3)(3/2) = -1/2
   c/a = -3/6 = -1/2
5. Final Result:
   Zeroes are -1/3 and 3/2

Q6. Find The Zeroes Of 4u² + 8u And Verify.

The zeroes are 0 and -2. Take 4u common before solving.

1. Given Data:
   Polynomial = 4u² + 8u
2. Formula Used:
   α + β = -b/a
   αβ = c/a
3. Calculation:
   4u² + 8u = 4u(u + 2)
   u = 0 or u = -2
4. Verification:
   Sum = 0 + (-2) = -2
   -b/a = -8/4 = -2
   Product = 0 × (-2) = 0
   c/a = 0/4 = 0
5. Final Result:
   Zeroes are 0 and -2

Q7. Find The Zeroes Of t² - 15.

The zeroes are √15 and -√15. Solve t² - 15 = 0.

1. Given Data:
   Polynomial = t² - 15
2. Formula Used:
   p(t) = 0
3. Calculation:
   t² - 15 = 0
   t² = 15
   t = ±√15
4. Final Result:
   Zeroes are √15 and -√15

Q8. Find The Zeroes Of 3x² - x - 4 And Verify.

The zeroes are 4/3 and -1. Factorise the quadratic polynomial.

1. Given Data:
   Polynomial = 3x² - x - 4
2. Formula Used:
   α + β = -b/a
   αβ = c/a
3. Calculation:
   3x² - x - 4 = (3x - 4)(x + 1)
   x = 4/3 or x = -1
4. Verification:
   Sum = 4/3 + (-1) = 1/3
   -b/a = -(-1)/3 = 1/3
   Product = (4/3)(-1) = -4/3
   c/a = -4/3
5. Final Result:
   Zeroes are 4/3 and -1

Relationship Between Zeroes And Coefficients Class 10 Questions

These relationship between zeroes and coefficients class 10 questions help solve problems without finding zeroes directly. They are common in CBSE 2026 exams.

Q1. If The Sum Of Zeroes Of 3x² - kx + 6 Is 3, Find k.

The value of k is 9. Use sum of zeroes = -b/a.

1. Given Data:
   Polynomial = 3x² - kx + 6
   Sum of zeroes = 3
2. Formula Used:
   Sum = -b/a
3. Calculation:
   Here, a = 3 and b = -k
   Sum = -(-k)/3
   Sum = k/3
   k/3 = 3
4. Final Result:
   k = 9

Q2. If α And β Are Zeroes Of ax² + bx + c, Find α² + β².

The value of α² + β² is (b² - 2ac)/a². Use the identity (α + β)² - 2αβ.

1. Given Data:
   Polynomial = ax² + bx + c
   Zeroes = α and β
2. Formula Used:
   α + β = -b/a
   αβ = c/a
   α² + β² = (α + β)² - 2αβ
3. Calculation:
   α² + β² = (-b/a)² - 2(c/a)
   α² + β² = b²/a² - 2c/a
   α² + β² = (b² - 2ac)/a²
4. Final Result:
   α² + β² = (b² - 2ac)/a²

Q3. Find k If The Sum Of Zeroes Of (k² - 14)x² - 2x - 12 Is 1.

The value of k is ±4. Apply the sum formula carefully.

1. Given Data:
   Polynomial = (k² - 14)x² - 2x - 12
   Sum of zeroes = 1
2. Formula Used:
   Sum = -b/a
3. Calculation:
   Sum = -(-2)/(k² - 14)
   2/(k² - 14) = 1
   k² - 14 = 2
   k² = 16
4. Final Result:
   k = ±4

Q4. What Is The Condition That Zeroes Of ax² + bx + c Are Reciprocal Of Each Other?

The condition is a = c. Reciprocal zeroes have product 1.

1. Given Data:
   Zeroes = α and 1/α
2. Formula Used:
   Product of zeroes = c/a
3. Calculation:
   α × 1/α = 1
   c/a = 1
   c = a
4. Final Result:
   a = c

Q5. If α And β Are Zeroes Of x² - 6x + y And 3α + 2β = 20, Find y.

The value of y is -16. Use the sum of zeroes first.

1. Given Data:
   Polynomial = x² - 6x + y
   3α + 2β = 20
2. Formula Used:
   α + β = -b/a
   αβ = c/a
3. Calculation:
   α + β = 6
   β = 6 - α
   3α + 2(6 - α) = 20
   α = 8
4. Find β And y:
   β = 6 - 8 = -2
   y = αβ
   y = 8 × (-2)
5. Final Result:
   y = -16

Q6. If Zeroes Of x³ - 3x² + x + 1 Are a - b, a, And a + b, Find a And b.

The values are a = 1 and b = ±√2. Use cubic zeroes relationships.

1. Given Data:
   Polynomial = x³ - 3x² + x + 1
   Zeroes = a - b, a, a + b
2. Formula Used:
   Sum of zeroes = -b coefficient/a coefficient
   Product of zeroes = -d/a
3. Calculation:
   (a - b) + a + (a + b) = 3a
   For x³ - 3x² + x + 1, sum = 3
   3a = 3
   a = 1
4. Product:
   (a - b)(a)(a + b) = a(a² - b²)
   Product = -1
   1(1 - b²) = -1
   b² = 2
5. Final Result:
   a = 1 and b = ±√2

Sum And Product Of Zeroes Class 10 Questions

These sum and product of zeroes class 10 questions cover direct polynomial formation. Use x² - (sum)x + product.

Q1. Find A Quadratic Polynomial With Sum -3 And Product 2.

The quadratic polynomial is x² + 3x + 2. Substitute the given sum and product.

1. Given Data:
   Sum = -3
   Product = 2
2. Formula Used:
   Polynomial = x² - (sum)x + product
3. Calculation:
   Polynomial = x² - (-3)x + 2
   Polynomial = x² + 3x + 2
4. Final Result:
   x² + 3x + 2

Q2. Find A Quadratic Polynomial With Sum 1/4 And Product -1.

The quadratic polynomial is 4x² - x - 4. Multiply by 4 to remove the fraction.

1. Given Data:
   Sum = 1/4
   Product = -1
2. Formula Used:
   Polynomial = x² - (sum)x + product
3. Calculation:
   Polynomial = x² - (1/4)x - 1
   Multiply by 4.
4. Final Result:
   4x² - x - 4

Q3. Find A Quadratic Polynomial With Sum √2 And Product 1/3.

The quadratic polynomial is 3x² - 3√2x + 1. Multiply by 3 to remove the denominator.

1. Given Data:
   Sum = √2
   Product = 1/3
2. Formula Used:
   Polynomial = x² - (sum)x + product
3. Calculation:
   Polynomial = x² - √2x + 1/3
   Multiply by 3.
4. Final Result:
   3x² - 3√2x + 1

Q4. Find A Quadratic Polynomial Whose Zeroes Are 3 + √2 And 3 - √2.

The quadratic polynomial is x² - 6x + 7. Use conjugate zeroes to simplify the product.

1. Given Data:
   Zeroes = 3 + √2 and 3 - √2
2. Formula Used:
   Polynomial = x² - (sum)x + product
3. Calculation:
   Sum = (3 + √2) + (3 - √2) = 6
   Product = (3 + √2)(3 - √2)
   Product = 9 - 2 = 7
4. Final Result:
   x² - 6x + 7

Q5. Find A Quadratic Polynomial Whose Zeroes Are -4 And -5.

The quadratic polynomial is x² + 9x + 20. The product is positive because both zeroes are negative.

1. Given Data:
   Zeroes = -4 and -5
2. Formula Used:
   Polynomial = x² - (sum)x + product
3. Calculation:
   Sum = -4 + (-5) = -9
   Product = (-4)(-5) = 20
   Polynomial = x² - (-9)x + 20
4. Final Result:
   x² + 9x + 20

Cubic Polynomial Class 10 Important Questions

These cubic polynomial class 10 important questions follow NCERT Section 2.3. Use only the relationship between zeroes and coefficients.

Q1. If Zeroes Of p(x) = 2x³ - 5x² - 14x + 8 Are 4, -2, And 1/2, Verify The Pairwise Product Relationship.

The relationship is verified. The sum of pairwise products equals c/a.

1. Given Data:
   Polynomial = 2x³ - 5x² - 14x + 8
   Zeroes = 4, -2, 1/2
2. Formula Used:
   αβ + βγ + γα = c/a
3. Calculation:
   αβ + βγ + γα = (4)(-2) + (-2)(1/2) + (1/2)(4)
   αβ + βγ + γα = -8 - 1 + 2
   αβ + βγ + γα = -7
4. Coefficient Check:
   c/a = -14/2
   c/a = -7
5. Final Result:
   The relationship is verified

Q2. If Zeroes Of p(x) = 2x³ - 16x² + 15x - 2 Are α - β, α, And α + β, Find α.

The value of α is 8/3. Use the sum of cubic zeroes.

1. Given Data:
   Polynomial = 2x³ - 16x² + 15x - 2
   Zeroes = α - β, α, α + β
2. Formula Used:
   Sum of zeroes = -b/a
3. Calculation:
   (α - β) + α + (α + β) = 3α
   For 2x³ - 16x² + 15x - 2, sum = 16/2
   3α = 8
4. Final Result:
   α = 8/3

Q3. If The Sum Of Zeroes Of ax³ + bx² + cx + d Is 5, What Is The Relation Between a And b?

The relation is b = -5a. Use the sum formula for cubic zeroes.

1. Given Data:
   Polynomial = ax³ + bx² + cx + d
   Sum of zeroes = 5
2. Formula Used:
   Sum of zeroes = -b/a
3. Calculation:
   -b/a = 5
   -b = 5a
   b = -5a
4. Final Result:
   b = -5a

Polynomials Class 10 Extra Questions With Solutions

These polynomials class 10 extra questions cover higher-order patterns based on zeroes, coefficients, and polynomial formation. They avoid the deleted Division Algorithm.

Q1. If α And β Are Zeroes Of x² + 5x + 2, Find (1/α + 1/β) - αβ.

The value is -9/2. Convert reciprocal sum into (α + β)/αβ.

1. Given Data:
   Polynomial = x² + 5x + 2
2. Formula Used:
   α + β = -b/a
   αβ = c/a
   1/α + 1/β = (α + β)/αβ
3. Calculation:
   α + β = -5
   αβ = 2
   1/α + 1/β = -5/2
   (1/α + 1/β) - αβ = -5/2 - 2
4. Final Result:
   -9/2

Q2. Find p In x² + 3x + p If One Zero Is 2.

The value of p is -10. Substitute the zero in the polynomial.

1. Given Data:
   Polynomial = x² + 3x + p
   Zero = 2
2. Formula Used:
   p(2) = 0
3. Calculation:
   2² + 3(2) + p = 0
   4 + 6 + p = 0
   p = -10
4. Final Result:
   p = -10

Q3. If α And β Are Zeroes Of 2x² - 5x + k And α² + β² + αβ = 21/4, Find k.

The value of k is 2. Use α² + β² + αβ = (α + β)² - αβ.

1. Given Data:
   Polynomial = 2x² - 5x + k
   α² + β² + αβ = 21/4
2. Formula Used:
   α + β = -b/a
   αβ = c/a
3. Calculation:
   α + β = 5/2
   αβ = k/2
   α² + β² + αβ = (α + β)² - αβ
   25/4 - k/2 = 21/4
4. Final Result:
   k = 2

Q4. If Zeroes Of x² + px + q Are Double The Zeroes Of 2x² - 5x - 3, Find p And q.

The values are p = -5 and q = -6. First find the original zeroes.

1. Given Data:
   Original polynomial = 2x² - 5x - 3
   New polynomial = x² + px + q
2. Formula Used:
   Polynomial = x² - (sum)x + product
3. Calculation:
   2x² - 5x - 3 = (2x + 1)(x - 3)
   Zeroes = 3 and -1/2
   Doubled zeroes = 6 and -1
4. New Polynomial:
   Sum = 5
   Product = -6
   x² + px + q = x² - 5x - 6
5. Final Result:
   p = -5 and q = -6

Q5. Does a⁴ + 4a² + 5 Have Real Zeroes?

The expression has no real zeroes. The related quadratic has a negative discriminant.

1. Given Data:
   Expression = a⁴ + 4a² + 5
2. Formula Used:
   Put a² = x
3. Calculation:
   x² + 4x + 5
   Discriminant = b² - 4ac
   Discriminant = 16 - 20
   Discriminant = -4
4. Final Result:
   No real zeroes exist

Class 10 Polynomials Previous Year Questions With Solutions

These class 10 polynomials previous year questions match recurring CBSE board patterns. They focus on zeroes, coefficients, and polynomial formation.

Q1. If The Sum Of Zeroes Of 3x² - kx + 6 Is 3, Find k.

The value of k is 9. Use the coefficient relationship for sum of zeroes.

1. Given Data:
   Polynomial = 3x² - kx + 6
   Sum = 3
2. Formula Used:
   Sum = -b/a
3. Calculation:
   Sum = k/3
   k/3 = 3
   k = 9
4. Final Result:
   k = 9

Q2. If α And β Are Zeroes Of ax² + bx + c, Find α² + β².

The value is (b² - 2ac)/a². Use the identity for sum of squares.

1. Given Data:
   Polynomial = ax² + bx + c
2. Formula Used:
   α² + β² = (α + β)² - 2αβ
3. Calculation:
   α + β = -b/a
   αβ = c/a
   α² + β² = b²/a² - 2c/a
   α² + β² = (b² - 2ac)/a²
4. Final Result:
   (b² - 2ac)/a²

Q3. If α + β = -6 And αβ = 5, Find The Polynomial.

The polynomial is x² + 6x + 5. Use the standard formation formula.

1. Given Data:
   Sum = -6
   Product = 5
2. Formula Used:
   Polynomial = x² - (sum)x + product
3. Calculation:
   Polynomial = x² - (-6)x + 5
   Polynomial = x² + 6x + 5
4. Final Result:
   x² + 6x + 5

Q4. Find The Condition That Zeroes Of ax² + bx + c Are Reciprocals.

The required condition is a = c. Reciprocal zeroes have product 1.

1. Given Data:
   Zeroes are reciprocal.
2. Formula Used:
   Product of zeroes = c/a
3. Calculation:
   c/a = 1
   c = a
4. Final Result:
   a = c

Q5. Find A Quadratic Polynomial With Sum √3 And Product 1/√3.

The polynomial is √3x² - 3x + 1. Multiply by √3 to remove the denominator.

1. Given Data:
   Sum = √3
   Product = 1/√3
2. Formula Used:
   Polynomial = x² - (sum)x + product
3. Calculation:
   Polynomial = x² - √3x + 1/√3
   Multiply by √3.
4. Final Result:
   √3x² - 3x + 1

Polynomials Class 10 Questions And Answers: Most Repeated Variations

These polynomials class 10 questions and answers cover recurring CBSE 2026 patterns. Students should practise graph zeroes, factorisation, and coefficient relationships.

Q1. What Are The Most Repeated Variations In Polynomials Class 10 Important Questions?

The most repeated variations are graph-based zeroes, factorisation, sum and product of zeroes, polynomial formation, and coefficient-based unknowns.

1. Graph Pattern:
   Count x-axis intersections.
2. Factorisation Pattern:
   Split the middle term and find zeroes.
3. Coefficient Pattern:
   Use α + β = -b/a and αβ = c/a.
4. Final Result:
   These five patterns cover most Chapter 2 board-style questions

Q2. How Should Students Solve Important Questions Class 10 Maths Chapter 2 With Solutions?

Students should identify whether the question uses graphs, factorisation, or coefficient relationships. Formula selection decides the solution path.

1. Read The Question:
   Check whether it asks for zeroes, coefficients, or polynomial formation.
2. Choose The Formula:
   Use graph rule, factorisation, or zeroes-coefficients relationship.
3. Substitute Carefully:
   Keep signs of b and c accurate.
4. Final Result:
   Sign accuracy decides most polynomial answers

Useful Important Questions Class 10 Maths Links