Question

if one zero of the polynomial (a2+9)x2+13x+6a is reciprocal of the other, find the value of A

Answer 1

$roots \: are \: \alpha \: \: and \: \: \frac{1}{ \alpha } \\ \alpha . \frac{1} { \alpha } = \frac{6a}{ {a}^{2} +9} \\ 1(a^{2} + 9) = 6a \\ {a}^{2} - 6a + 9 = 0 \\ {(a - 3)}^{2} = 0 \\ a = 3$