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

Zeroes of polynomial means for what value of x the equation becomes 0

The polynomial given is quadratic since the degree is 2

Let one zero of polynomial be α

As the other is its reciprocal hence

Compare (a² + 9)x² + 13x + 6a with standard form of quadratic equation px² + qx + r

p = a² + 9, q = 13 and r = 6a

product of roots of quadratic

⇒ r = p

⇒ 6a = a² + 9

⇒ a² – 6a + 9 = 0

⇒ a² – 2(3)a + 3² = 0

Using (a – b)² = a² – 2ab + b²

⇒ (a – 3)² = 0

⇒ a = 3

Hence a = 3