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Nature of Roots

The value of ...

Question

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

(a) $\frac{b^{2}}{a}$
(b) $\frac{b^{2}}{4 a}$
(c) $\frac{a^{2}}{b}$
(d) $\frac{a^{2}}{4 b}$

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Solution

The given quadric equation is , and roots are equal

Then find the value of c.

Let be two roots of given equation

Then, as we know that sum of the roots

And the product of the roots

Putting the value of

Therefore, the value of

Thus, the correct answer is

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