Search any question & find its solution
Question:
Answered & Verified by Expert
If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^{3}+4 x+2=0$, then $\alpha^{3}+\beta^{3}+\gamma^{3}$ is equal to
Options:
Solution:
2738 Upvotes
Verified Answer
The correct answer is:
$-6$
Given, $x^{3}+4 x+2=0$
$\therefore \quad \Sigma \alpha=0, \quad \Sigma \alpha \beta=\frac{4}{1}=4, \quad \alpha \beta \gamma=\frac{-2}{1}=-2$
$\because \quad \Sigma \alpha=0$
$\therefore \quad \alpha^{3}+\beta^{3}+\gamma^{3}=3 \alpha \beta \gamma=3(-2)=-6$
$\therefore \quad \Sigma \alpha=0, \quad \Sigma \alpha \beta=\frac{4}{1}=4, \quad \alpha \beta \gamma=\frac{-2}{1}=-2$
$\because \quad \Sigma \alpha=0$
$\therefore \quad \alpha^{3}+\beta^{3}+\gamma^{3}=3 \alpha \beta \gamma=3(-2)=-6$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.