Question

The value of c for which the equation ax² + 2bx + c = 0 has equal roots is

Options

• \[\frac{b^2}{a}\]

• \[\frac{b^2}{4a}\]

• \[\frac{a^2}{b}\]

• \[\frac{a^2}{4b}\]

Answer 1

The given quadric equation is ax² + 2bx + c = 0 , and roots are equal

Then find the value of c.

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

Then, as we know that sum of the roots

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

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

      `2alpha = (-2b)/a`

        `alpha = (-b)/a`

And the product of the roots

`alpha . beta = c/a`

`alpha alpha = c /a`

Putting the value of `alpha `

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

                `b^2/a = c`

Therefore, the value of ` c =b^2/a`