Question

If ax² + bx + c = 0 has equal roots, then c =

Options

• \[\frac{- b}{2a}\]

• \[\frac{b}{2a}\]

• \[\frac{- b^2}{4a}\]

• \[\frac{b^2}{4a}\]

Answer 1

The given quadric equation is ax² + 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)`.