Question

lf $\alpha ,\beta ,\gamma$ are the roots of $x^3+x^2+x+1=0$ then ${\alpha }^3+{\beta }^3+{\gamma }^3=$

• A. $1$
• B. $-1$
• C. $2$
• D. $-2$

Answer 1

Answer: (B)

$-1$

Given equation $x^3+x^2+x+1=0$ has roots $\alpha ,\beta ,\gamma$

Substitute them in equation

We get $\sum {\alpha }^3=-\left[\right(\sum \alpha {)}^2-2\sum \alpha \beta +\sum \alpha +3]$

$\sum \alpha =-[-1-1+3]$

$\sum \alpha =-1$