First slide

Theory of expressions

Question

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

Moderate

A

$3 p q + p^{3}$
B

$3 p q - p^{3}$
C

$3 p q$
D

$p^{3} - 3 p q$

Solution

$α + β = - p, α β = q$
Now, $α^{3} + β^{3} = (α + β)^{3} - 3 α β (α + β)$
$= - p^{3} + 3 p q = 3 p q - p^{3}$

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