If one zero of the polynomial $p (x) = 5 x^{2} + 13 x - a$ is the reciprocal of the other, find the value of $a$ .

5

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Solution

The correct option is D $- 5$
Given that,
$p (x) = 5 x^{2} + 13 x - a$
Here, $a = 5, b = 13$ & $c = - a$

Let, the zeroes are $α, \frac{1}{α}$

Product of zeroes $(α \times \frac{1}{α}) = \frac{c}{a}$

$⟹ 1 = \frac{- a}{5}$

$⟹ 5 = - a$

$∴ a = - 5$

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