Question

$\alpha$ and $\beta$ are the roots of $x^2+2x+C=0$. If ${\alpha }^3+{\beta }^3=4$, then the value of $C$ is

• A. $-2$
• B. $3$
• C. $2$
• D. $4$

Answer 1

Answer: (C)

$2$

Given equation is $x^2+2x+C=0$ and ${\alpha }^3+{\beta }^3=4$

Therefore, $\alpha +\beta =-2;\alpha \beta =C$

Thus ${\alpha }^3+{\beta }^3=4$

$\Rightarrow {(\alpha +\beta )}^3-3\alpha \beta (\alpha +\beta )=4$

$\Rightarrow -8-3C(-2)=4$

$\Rightarrow 6C=12$

$\Rightarrow C=2$