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Quantitative Aptitude

Equations

If α, β,γ a...

Question

If $α, β, γ$ are the roots of the equation $x^{3} - p x^{2} + q x - r = 0$ , then the value of $\sum α^{2} β$ is equal to

A

p q + 3 r

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B

p q + r

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C

p q - 3 r

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D

q^{2} / r

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Solution

The correct option is C $p q - 3 r$
$α + β + γ = p; α β + α γ + β γ = q; α β γ = r$
$\sum α^{2} β = α^{2} β + β^{2} α + β^{2} γ + β γ^{2} + α^{2} γ + α γ^{2} = (\sum α) (\sum α β) - 3 α β γ = p q - 3 r$

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