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Mathematics

If the roots of the quadratic equation, ax2 + bx + c = 0, a ≠ 0 are real and equal, then each root is equal to:

  1. −a2b\dfrac{-a}{2b}

  2. −b2a\dfrac{-b}{2a}

  3. −2ab\dfrac{-2a}{b}

  4. −c2a\dfrac{-c}{2a}

Quadratic Equations

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Answer

Let us consider the quadratic equation ax2 + bx + c = 0, a ≠ 0 and a, b, c are real numbers.

Let r1 and r2 be the roots of this equation.

r1 = −b+D2a\dfrac{-b + \sqrt{D}}{2a}

r2 = −b−D2a\dfrac{-b - \sqrt{D}}{2a}

if the roots are real and equal then D = 0,

r1 = −b+02a\dfrac{-b + \sqrt{0}}{2a}

r1 = −b2a\dfrac{-b}{2a}

r2 = −b−02a\dfrac{-b - \sqrt{0}}{2a}

r2 = −b2a\dfrac{-b}{2a}

r1 = r2 = −b2a\dfrac{-b}{2a}

Hence, each root can be given by −b2a\dfrac{-b}{2a}.

Hence, option 2 is the correct option.

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