Question

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

Answer 1

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 × 1/α = 6a/(a²+9)
⇒ 1 = 6a/(a²+9)
⇒ a² + 9 = 6a
⇒ a² - 6a + 9 = 0
⇒ a² - 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.