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