Question

If $\alpha ,\beta$ and $\gamma$ are the roots of the equation $x^3+4x+2=0$, then ${\alpha }^3+{\beta }^3+{\gamma }^3$ is equal to

• A. $2$
• B. $6$
• C. $-2$
• D. $-6$

Answer 1

The correct option is D

$-6$

Explanation for the correct option:

Find the value of ${\alpha }^3+{\beta }^3+{\gamma }^3$:

Given, $x^3+4x+2=0$

Here, $\sum \alpha =0$

$\begin{array}{rcl}\sum \alpha \beta & =& \frac{4}{1}\\ & =& 4\end{array}$

$\begin{array}{rcl}\alpha \beta \gamma & =& \frac{-2}{1}\\ & =& -2\end{array}$

As we know,

$\begin{array}{rcl}{\alpha }^3+{\beta }^3+{\gamma }^3& =& 3ɑ\beta \gamma \\ & =& 3\times \left(-2\right)\\ & =& \mathbf{-}\mathbf{6}\end{array}$

Hence, Option ‘D’ is Correct.