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The roots of equation $a x^{2} + x + b = 0$ will be equal if :

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$b^{2} = 14$

ab = 1/4

$b^{2} + 9 = 0$

12 + a = 3

answer is A.

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Detailed Solution

We have $a x^{2} + x + b = 0$

$\Rightarrow$ for equal and real roots, $b^{2} - 4 a c = 0$

$\Rightarrow b^{2} = 4 a c$

$\Rightarrow b^{2} = 4 a c$ b = 1, a = a and c = b.

$\Rightarrow$ 1 = 4ab

$\Rightarrow a b = \frac{1}{4}$

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