Question

If one zero of a polynomial (a+5)x^2+13x+6a is reciprocal of the other find a

Answer 1

The vaue of a is "1".

Step-by-step explanation:

Let α and $\frac{1}{α}$ be the reciprocal of quadratic polynomial.

We know that,

Product of zeroes = $\frac{c}{a}$

⇒ α·$\frac{1}{α}$ = $\frac{6a}{a +5}$

⇒ 1 = $\frac{6a}{a +5}$

⇒ a + 5 = 6a

⇒ 5a - a = 5a  = 5

⇒ a = 1

Hence, the vaue of a is "1".