If the product of the roots of $4 x^{3} + 16 x^{2} - 9 x - a = 0$ is $9$ , then find $a$ .

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Solution

Fact: Product of roots of $a x^{3} + b x^{2} + c x + d = 0$ is $- \frac{d}{a}$

So the product of roots of $4 x^{3} + 16 x^{2} - 9 x - a = 0$ is $= - \frac{- a}{4} = 9$ (given)
$\Rightarrow a = 36$

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