Question

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

Answer 1

product of root is 2 roots are reciprocal of each other is 1...
from question
product of roots= 6a/(a2+9)= 1
6a= a2+9
a2-6a+9= 0
(a-3)²= 0
a=3....is the answer..

Answer 2

Hey


Given equation is :-


( a² + 9 )x² + 13x + 6a


Now ,


Solution :-


Let the first zero be y

So , second zero be 1 / y ( reciprocal of first )


Now ,

y * 1 / y = 6a / a² + 9


=> 6a = a² + 9


=> a² - 6a + 9 = 0


=> a ² - 3a - 3a + 9 = 0


=> a ( a - 3 ) - 3 ( a - 3 ) = 0


=> ( a - 3 ) ( a - 3 ) = 0


So ,

a = 3


thanks :)