Quadratic equation １０

2x^2 + 5x - 4 = 0
Sum of roots = α + β = -5/2
Product of roots αβ = -4/2 = -2
(a)α^2 - αβ + β^2
= α^2 + 2αβ + β^2 - 3αβ
= (α + β)^2 - 3αβ
= 25/4 + 6
= 49/4
(b)2α^2 + 5αβ + 2β^2
= 2α^2 + 4αβ + 2β^2 + αβ
= 2(α^2 + 2αβ + β^2) + αβ
= 2(α + β)^2 + αβ
= 2(25/4) - 2
= 21/2