Solution of Quadratic Equations
A number ? is said to be the root of a quadratic equation ax2 + bx + c = 0, if a?2 + b? + c = 0.
A quadratic polynomial can have at most two zeroes. Any quadratic equation can have at most two roots.
A quadratic equation has exactly two roots: equal or distinct; real or imaginary.
Discriminant (D) = b2 – 4ac
Nature of roots when D > 0 is two distinct real roots.
Nature of roots when D = 0 is two equal real roots.
Nature of roots when D < 0 is no real roots.
Sum of roots is given by ? + ? = –b/a = – (coefficient of x) / (coefficient of x2)
Product of roots is given by ?? = c/a = (constant term) / (coefficient of x2)
Therefore, a quadratic equation can be written as x2 – (sum of roots)x + (product of roots) = 0.
If ?, ? are the roots of a quadratic equation ax2 + bx + c = 0, where a ? 0, then the expression of the form ? + ?, ??, ?2 ? ?2, etc. are called functions of the roots ? and ?.
Keywords: Quadratic Equation Formula, Reciprocal roots, Zero roots, Infinite roots, Positive roots, Negative roots, Roots of opposite sign, Roots equal in magnitude but opposite in sign, Common roots
To Access the full content, Please Purchase

Q1
Solve the equation x^{2}  9 = 0.
Marks:1Answer:
x^{2}  9 = 0
(x  3)(x + 3) = 0
x = 3 and x = 3 
Q2
Product of two consecutive positive integers is 240. Find the integers.
Marks:1Answer:

Q3
Solve the equation 3x^{2}  2x  1 = 0.
Marks:1Answer:
3x^{2}  2x  1 = 0
3x^{2}  3x + x  1 = 0
3x(x  1) + (x  1) = 0
(x  1)(3x + 1) = 0
x = 1 and x = 1/3 
Q4
Find the discriminant of the quadratic equation
4x^{2 } 17x + 4 = 0.Marks:1Answer:

Q5
Find the discriminant of the quadratic equation:
x^{2}3x10=0
Marks:1Answer: