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If one root of $x^{2} + a x + 8 = 0$ is 4 and the equation $x^{2} + a x + b = 0$ has equal roots, then $b =$

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answer is B.

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Detailed Solution

Let $x = 4$

$\Rightarrow 4^{2} + 4 a + 8 = 0$

$\Rightarrow a = - 6$

The roots of $x^{2} + a x + b = 0$ are equal

$\Rightarrow Δ = 0$

$\Rightarrow a^{2} - 4 b = 0$

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

$\Rightarrow {(- 6)}^{2} = 4 b$

$\Rightarrow b = 9$

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