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 is equal to

Correct option is 4−f(α)f(β)f(γ)

Questions

If $f (x) = a + bx + {cx}^{2}$ and $α, β, γ$ are the roots of the equation $x^{3} = 1, then |\begin{array}{lll} a b c \\ b c a \\ c a b \end{array}|$ is equal to

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f(α)+f(β)+f(γ)

f(α)f(β)+f(β)f(γ)+f(γ)f(α)

f(α)f(β)f(γ)

−f(α)f(β)f(γ)

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detailed solution

Correct option is D

abcbcacab=−a3+b3+c3−3abc=−(a+b+c)a+bω2+cωa+bω+cω2 (where ω is cube roots of unity) =−f(α)f(β)f(γ) ∵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 is equal to

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Ready to Test Your Skills?

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If $f (x) = a + bx + {cx}^{2}$ and $α, β, γ$ are the roots of the equation $x^{3} = 1, then |\begin{array}{lll} a b c \\ b c a \\ c a b \end{array}|$ is equal to