Question

If any zero of the polynomial a square+9 whole x square +13x+6x+6a is reciprocal of the other,find the value of a

Answer 1

f 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.