If α and β be the roots of the equation ax 2 + bx + c = 0, find the value of α 2/β + β 2/α .

Given, α and β are the roots of the equation ax² + bx + c = 0
∴ Sum of two roots = -b/a
α + β = -b/a
and product of two roots = c/a
α β = c/a
∴ α²/β + β²/α = ( α³ + β³) / α β
= [(α + β) ³ - 3 α β (α + β)] / αβ
[∵ (a + b)³ = a³ + b³ + 3ab(a + b) ]
= (-b/a)³ - [3c/a(-b/a)/c/a = -b³/a³ + 3bc/a²]/(c/a)
= 3abc - b³/a²c