Question

If one zero of polynomial bracket a square + 9 bracket close X square + 13 x + 6 is reciprocal of other find the value of a

Answer 1

hope it will help you !!

Answer 2

Heya

The polynomial is
$p(x) = ( {a}^{2} + 9) {x}^{2} + 13x + 6a$
By definition of reciprocal, one root is the multiplicative inverse of the other

=> Product of roots = 1

But, by root - coefficient relation,
$\frac{6a}{( {a}^{2} + 9) } = 1$
$= > {a}^{2} - 6a + 9 = 0$

$= > {(a - 3)}^{2} = 0$

$= > a = 3$

Hope it helps