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Relation between Roots and Coefficients for Quadratic

If α, β are t...

Question

If $α$ , $β$ are the roots of $x^{2} + p x + q = 0$ , then the value of $α^{3} + β^{3}$ is

A

3 p q + p^{3}

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B

3 p q - p^{3}

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C

3 p q

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D

p^{3} - 3 p q

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Solution

The correct option is B $3 p q - p^{3}$
$x^{2} + p x + q = 0$
Now the sum of roots and product of roots is,
$α + β = - p$ , $α β = q$
So,
$α^{3} + β^{3} = (α + β)^{3} - 3 α β (α + β) \Rightarrow α^{3} + β^{3} = - p^{3} - 3 q (- p) ∴ α^{3} + β^{3} = 3 p q - p^{3}$

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Relation between Roots and Coefficients for Quadratic

Standard XIII Mathematics

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