#### Question

If ax^{2} + bx + c = 0 has equal roots, then c =

\[\frac{- b}{2a}\]

\[\frac{b}{2a}\]

\[\frac{- b^2}{4a}\]

\[\frac{b^2}{4a}\]

#### Solution

The given quadric equation is ax^{2} + bx + c = 0 , and roots are equal

Then find the value of *c.*

Let `alpha = beta `be two roots of given equation

Then, as we know that sum of the roots

`alpha + beta = (-b)/ a`

`alpha + alpha = (-b)/ a`

`2alpha = (-b)/ (2a)`

`alpha = (-b)/ (2a)`

And the product of the roots

`alpha. beta = c/a`

`alpha alpha = c / a`

Putting the value of `alpha`

`(-b)/(2a) xx (-b)/(2a) = c/a`

`b^2/4a = c`

Therefore, the value of `c = (b^2)/(4a)`.

Is there an error in this question or solution?

#### APPEARS IN

Solution If Ax2 + Bx + C = 0 Has Equal Roots, Then C = Concept: Solutions of Quadratic Equations by Factorization.