If the polynomial $f (x) = 2 x^{3} + m x^{2} + n x - 14$ has $(x - 1)$ and $(x + 2)$ as its factors, find the value of $\frac{m}{n}$ .

27

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\frac{1}{3}

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3

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\frac{1}{27}

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Solution

The correct option is C $3$
$f (1) = 0 \Rightarrow m + n = 12$
$f (- 2) = 0 \Rightarrow 2 m - n = 15$
$\Rightarrow m = 9; n = 3 ∴ \frac{m}{n} = 3$ .

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