Question

If Alpha and Beta are the zeroes of the quadratic polynomial p(x) = 4x^2-5x-1, find the value of (Alpha)^2 * Beta + Alpha * (Beta)^2

Answer 1

Answer

If α,β are the zeros of p(x)=4x

2

−5x−1

Then α+β=

4

5

,αβ=−

4

1

α

2

β+αβ

2

=(αβ)(α+β)=−

16

5