Question

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

पर्याय

• $$\frac{b^2}{a}$$

• $$\frac{b^2}{4a}$$

• $$\frac{a^2}{b}$$

• $$\frac{a^2}{4b}$$

Answer 1

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

Then find the value of c.

Let ${\displaystyle \alpha \text{and}\beta }$ be two roots of given equation ${\displaystyle \alpha =\beta }$

Then, as we know that sum of the roots

${\displaystyle \alpha +\beta =\frac{-2b}{a}}$

${\displaystyle \alpha +\alpha =\frac{-2b}{a}}$

      ${\displaystyle 2\alpha =\frac{-2b}{a}}$

        ${\displaystyle \alpha =\frac{-b}{a}}$

And the product of the roots

${\displaystyle \alpha .\beta =\frac{c}{a}}$

${\displaystyle \alpha \alpha =\frac{c}{a}}$

Putting the value of ${\displaystyle \alpha }$

${\displaystyle \frac{-b}{a}\times \frac{-b}{a}=\frac{c}{a}}$

                ${\displaystyle \frac{b^2}{a}=c}$

Therefore, the value of ${\displaystyle c=\frac{b^2}{a}}$