Question

If one zero of the polynomial (a^2 + 9)x^2 + 13x +6a is reciprocal of the other then find the value of a.

Answer 1

Given polynomial :

p(x) = (a²+9)x²+14x+6a

To Find : .

The value of a if one zero of the polynomial is reciprocal of the first zero.

Solution :

Let the first zero = α

Then the second zero = ¹/α

We know the relationship between the product of zeroes and the coefficients of the polynomial.

Using that we can find out the value of a.

For full solution refer to the above attachment.

Answer 2

Answer:

a=3

Step-by-step explanation:

let the first zero be alpha and the second zero be 1/alpha.

so we know that

alpha×1/alpha=c/a

alpha×i/alpha=6a/a2+9

a2=9-6a=1

a2-6a+9=1

a2-6a+9=1

a2-3a-3a+9=1

a(a-3)-3(a-3)=1

(a-3)(a-3)=1

∴ a=3 ; a=3

∴ the value of a is 3.