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If α and β be the roots of the equation ax2 + bx + c = 0, find the value of α2/β + β2/α .
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- ab -b2c/2b2c
- 3bc - a3/b2c
- 3ac - b2/a3c
- 3abc - b3/a2c
- None of the above
Correct Option: D
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
