In the following equation if two zeros of polynomial are reciprocal to each other then find the value of 'a'. (a^2 9)x^2 13x 6a?

Question

Answer

If one of the zero is reciprocal of the other,

let one zero be α

other zero will be 1/α

Product of roots = c/a

⇒ α x 1/α = 6a/(a^2+9)

⇒ 1 = 6a/(a^2+9)

⇒ a^2 + 9 = 6a

⇒ a^2 - 6a + 9 = 0

⇒ a^2 - 3a - 3a + 9= 0

⇒ a(a-3) -3(a-3) = 0

⇒ (a-3)(a-3) = 0

⇒ (a-3)^2= 0

⇒ a = 3

Value of a is 3.