Question

if one zero of the polynomial (a+9)x²+39x+6a is the reciprocal of the other. find the value of a

Answer 1

let that zero is $\alpha$and other zero is $\frac{1}{ \alpha }$
product of zeros
$\alpha \times \frac{1}{ \alpha } = \frac{c}{a} = \frac{6a}{a + 9} \\ 1 = \frac{6a}{a + 9} \\ a + 9 = 6a \\ a - 6a = - 9 \\ - 5a = - 9 \\ a = \frac{9}{5}$