Question

if one of the zero of a polynomial p(x)=(a^2+9)x^2+45x+6a is recipocal of the other find a

Answer 1

$since \: one \: zero \: is \: reciprocal \: of \: other \\ product \: of \: zeros \: is \: 1 \\ \frac{6a}{ {a}^{2} + 9} = 1 \\ {a}^{2} - 6a + 9 = 0 \\ {(a - 3)}^{2} = 0 \\ a = 3$