Given: x2 – 5x + 6 = 0
On comparing this equation with ax2 + bx + c = 0, we get:
a = 1, b = –5 and c = 6
α and β are the roots of the equation.
To find the value of α2 + β2, we need to express it in terms of (α + β) and αβ because we know that α + β = – and αβ = .
Thus,
α2 + β2 = α2 + β2 + 2αβ – 2αβ
α2 + β2 = (α + β)2 – 2αβ
On substituting α + β = – and αβ = , we get:
α2 + β2 =
On substituting a = 1, b = –5 and c = 6, we get: