f.4 quad. equation15marks!!!!!

2x^2 - 6x + 3 = 0
Sum of roots α+β = 6/2 = 3
Product of roots αβ = 3/2
(a) α^2 + β^2
= α^2 + β^2 + 2αβ - 2αβ
= (α + β)^2 - 2αβ
= 3^2 - 2(3/2)
= 6
(b) (α - β)^2
= α^2 + β^2 - 2αβ
= 6 - 2(3/2)
= 3
(c) (α - β)^2 = 3
α - β = √3 since α > β
(d) α^4 - β^4
= (α^2 - β^2)(α^2 + β^2)
= (α - β)(α + β)(α^2 + β^2)
= √3(3)(6)
= 18√3