Question

If α, β are the roots of ax2 − 2bx + c = 0 then α3β3 + α2β3 + α3β2 is(a) 2 ( )3c c 2ba+ (b)33bca(c)23ca(d) None of these

Answer 1

Sum of roots  = α+β = 2b/a
Product of roots = αβ = c/a

α³β³ + α²β³ + α³β²
= (αβ)³ + (αβ)²(α+β)
= (c/a)³ + (c/a)² (2b/a)
= (c/a)²[ (c/a) + (2b/a) ] 
= (c/a)²[ (c+2b)/a]
= $\frac{c^2(c+2b)}{a^3}$

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