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Nature of Roots

α, β are the ...

Question

$α, β$ are the roots of the equation $x^{2} + 4 x + 5.$ Find the value of $α^{3} + β^{3}$

A

4

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B

-4

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C

6

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D

-6

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Solution

The correct option is B
-4

Sum of the roots, $α + β = - 4$ ... (i)

Product of the roots, $α β = 5$ ... (ii)

Taking cube of equation (i)

${(α + β)}^{3} = α^{3} + β^{3} + 3 α β (α + β)$

$\Rightarrow α^{3} + β^{3} = {(α + β)}^{3} - 3 α β (α + β)$

$= {(- 4)}^{3} - 3 \times 5 \times - 4$

$= - 64 + 60$

$= - 4$

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