TS EAMCET 7 May 2018 Shift 1 Solved Paper

Given:
x4−10x3+37x2−60x+36=0
The roots of the equation are α,α,β,β.
The sum of all the roots is,
α+α+β+β=

−(−10)

1

2(α+β)=10
α+β=5
The multiple of all the roots is,
α2β2=36
αβ=6
Substitute (5−α) for β in above equation.
α(5−α)=6
5α−α2=6
α=2,3
β=3,2
As (α<β),α=2,β=3
2α+3β−2αβ=4+9−12
=4+9−12
=1