If $α$ and $\frac{1}{α}$ are zeroes of polynomial $3 x^{2} + 13 x + (12 - p)$ . What is the value of $p$ ?

12

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13

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9

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10

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Solution

The correct option is C $9$
In the given polynomial, $3 x^{2} + 13 x + (12 - p)$
$a = 3, b = 13, c = 12 - p$
Applying relationship between zeroes and coefficient of the polynomial:
Product of the zeroes $(α \times \frac{1}{α}) = \frac{c}{a}$
$1 = \frac{12 - p}{3}$
$3 = 12 - p$
$p = 12 - 3$
$p = 9$

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