If α,β are the zeros of the polynomial 2x^{2} - 4x + 5 find the value of a) α^{2} + β^{2} b) (α - β)^{2}.
Ans: p (x) = 2 x^{2} - 4 x + 5 (Ans: a) -1 , b) -6)
α + β = -b /a = 4/2 = 2
α β = c/a = 5/2
α^{2} + β^{2} = (α + β)^{2} - 2 α β
Substitute then we get, α ^{2}+ β^{2} = -1
(α - β)^{2} = (α + β)^{2} - 4 α β
Substitute, we get = (α - β)^{2} = - 6