Answer:

hope you understood it. don't comment on my writing it's good.

Step-by-step explanation:

Given, α,β are zeroes of the polynomial p(x)=x

2

−x−4, Then from the relation between the relation roots and co-efficients we get,

α+β=1.....(1) and α.β=−4......(2).

Now,

β

α

+

α

β

+3(

α

1

+

β

1

)−2αβ

=

α.β

α

2

+β

2

+3

α.β

α+β

−2α.β

=

α.β

(α+β)

2

−2α.β

+3

α.β

α+β

−2α.β

=−

4

9

−

4

3

+8 [ Using (1) and (2)]

=−3+8

=5.