If $^{'} 2^{'}$ is repeated root of the cubic equation $3 x^{3} + p x^{2} + q x - 12 = 0$ Then the value of $p + q$ is

9

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27

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3

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N . O . T

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Solution

The correct option is A $9$
$3 x^{3} + p x^{2} + q x - 12 = 0$
$2$ occurs a minimum of $2$ times
Product of roots $= \frac{- (- 12)}{3} = \frac{12}{3} = 4$
$2 \times 2 \times$ other root $= 4$
Other root $= \frac{4}{4} = 1$
$∴$ Roots are $2, 2, 1$
Sum $= 2 + 2 + 1 = 5 = \frac{- p}{3}$
$p = - 15$
Sum of products $= 2 (2) + 2 + 2$
$= 8 = \frac{q}{3}$
$q = 24$
$p + q = 24 - 15 = 9$

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