If the polynomial $f (x) = a x^{3} + b x - c$ is divisible by the polynomial $g (x) = x^{2} + b x + c,$ then $a b =$

- \frac{1}{c}

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- 1

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1

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\frac{1}{c}

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Solution

The correct option is C $1$
$f (x) = a x^{3} + b x - c$
$= a x^{3} + o x^{2} + b x - c$
$g (x) = x^{2} + b x + c$
Dividing $f (x)$ by $g (x)$

$∵ f (x)$ is completely divisible by $g (x)$
$∴ r (x) = 0$
$(b - a c + a b^{2}) x + a b c - c = 0$
$b - a c + a b^{2} = 0$ and $a b c - c = 0$
$\Rightarrow a b c = c \Rightarrow a b = 1$

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