Question

If one zero of the polynomial (a

2 + 9)x

2 +13x +6a is reciprocal of the other,find the value of a.​

Answer 1

Answer:

If one zero of the polynomial (a2 + 9)x2 + 13x + 6a is reciprocal of the other, then the value of a is 3.

According to the question, one of the zeroes is reciprocal of the other, so, let us consider one zero to be x.

Therefore, the other zero will be 1 / x, and the product of zeroes will be 1.

For any polynomial of the form ax2+ bx + c = 0,

Sum of zeroes = - b / a

Product of zeroes = c / a

Using these results for the equation given in the question (a2 + 9)x2 + 13x + 6a, we get

The product of zeroes will be c / a = 6a / a2+ 9 = 1

⇒ a2+ 9 = 6a

⇒ a2- 6a + 9 = 0 [rearranging terms]

⇒ a2 – 3a – 3a + 9 = 0 [splitting middle term]

⇒ a (a - 3) -3 (a - 3) = 0 [taking a as common in 1st two terms and - 3 as common in last two terms]

⇒ (a - 3) (a - 3) = 0

⇒ a = 3 , 3

Hence, the value of a is 3