Question

IS ONE ZERO OF THE POLYNOMIAL p[x]=[a2+9]x2+45x+6a is reciprocal of the other.Find the value of a.

Answer 1

$( {a}^{2} + 9) {x}^{2} + 45x + 6a = 0$
Let the zeroes be
$\alpha \: \: \: \: \: \: \frac{1}{ \alpha }$
Now
$\alpha \times \frac{1}{ \alpha } = \frac{6a}{ {a}^{2} + 9} \\ {a}^{2} + 9 - 6a = 0 \\ {(a - 3)}^{2} = 0 \\ a = 3$
Mark it as the brainliest answer.