If one zero of the polynomial (a square+9)x square +13x+6a is reciprocal of the other, find the value of a

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.

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