Question

If alfa and beta are the zeros of the quadratic polynomial f(x)=6x²+x-2, find alfa/beta + beta/alfa.

Answer 1

Hope it helps you...

Answer 2

We have,p(x) = 6x2 + x − 2

Sum of zeroes = α + β = coefficient of x /coefficient of x^2
α + β= -b/a

Product of zeroes = αβ = constant term /coefficient of x^2

αβ = c/a

Now,

α + β = -1/6

αβ = -1/3

α / β + β / α= α^2+β ^2/αβ
So,

==> [ (α+β )^2 - 2αβ ] /αβ

Putting the value

==> [ ( -1/6)^2 +2/3] / - 1/3

==> [1/36+2/3] / -1/3
==>[ 25/36] /-1/3

==> 25/36×-1/3

==> -25/12 Ans