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

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  • Q1

    Solve the equation x2 - 9 = 0.

    Marks:1
    Answer:

    x2 - 9 = 0
    (x - 3)(x + 3) = 0
    x = 3 and x = -3

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  • Q2

    Product of two consecutive positive integers is 240. Find the integers.

    Marks:1
    Answer:

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  • Q3

    Solve the equation 3x2 - 2x - 1 = 0.

    Marks:1
    Answer:

    3x2 - 2x - 1 = 0
    3x2 - 3x + x - 1 = 0
    3x(x - 1) + (x - 1) = 0
    (x - 1)(3x + 1) = 0
    x = 1 and x = -1/3

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  • Q4

    Find the discriminant of the quadratic equation
    4x2 - 17x + 4 = 0.

    Marks:1
    Answer:

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  • Q5

    Find the discriminant of the quadratic equation:

    x2-3x-10=0

    Marks:1
    Answer:

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