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Q.

If f(x)=a+bx+cx2 and α,β,γ are the roots of the equation x3=1, then a    b    cb    c    ac    a    b  equal to

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a

f(α)+f(β)+f(γ)

b

f(α)f(β)+f(β)f(γ)+f(γ)f(α)

c

f(α)f(β)f(γ)

d

−f(α)f(β)f(γ)

answer is D.

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Detailed Solution

abcbcacab=−a3+b3+c3−3abc=−(a+b+c)a+bω2+cωa+bω+cω2=−f(α)f(β)f(γ)  (where ω is cube roots of unity) ∵α=1,β=ω,γ=ω2
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If f(x)=a+bx+cx2 and α,β,γ are the roots of the equation x3=1, then a    b    cb    c    ac    a    b  equal to