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Quantitative Aptitude

Quadratic Equations

If α and β ar...

Question

If $α a n d β$ are the roots of the equation $x^{2} - 2 x + 4 = 0,$ then what is the value of $α^{3} + β^{3} ?$

A

16

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B

-16

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C

8

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D

-8

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Solution

The correct option is B -16
$(α + β)$ = 2 and $α β = 4$
Use $α^{3} + β^{3} = (α + β)^{3} - 3 α β (α + β)$ = 8 - 24 = -16

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