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Relation between Roots and Coefficients for Quadratic

α, β are the ...

Question

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

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 C
-4

α + β = -4

αβ = 5

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

⇒ $α^{3}$ + $β^{3}$ = ${(α + β)}^{3}$ - 3αβ(α + β)

= ${(- 4)}^{3}$ - 3 × (5) × (-4)

= -64 + 60

= - 4

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