Question

If one zero of a polynomial a square + 9 into x square + 13 x + 6 is reciprocal of other then find the value of a

Answer 1

Given ,

One of the zero of the polynomial is reciprocal of the other.

And the given expression is quadriatic in X with the zeroes of the polynomial being it's roots.

We know that , product of roots of a quariatic , ax^2 + bx + c = 0 is given by c/a.

SO , here ,

AS the zeroes are reciprocal to each other , their product = 1

So, 6a/(a^2 + 9) = 1

a^2-6a + 9 = 0

(a-3)^2 = 0

a = 3