Question

If $\alpha ,\beta$ are the roots of $x^2+px+q=0$ then ${\alpha }^3+{\beta }^3=$

• A. $p+q^3$
• B. $p+3p^{3}q$
• C. $-p^3+3pq$
• D. $p^2-3pq$

Answer 1

The correct option is C $-p^3+3pq$

Let $\alpha ,\beta$ be the roots of the equation $x^2+px+q=0$

sum of the roots$=\alpha +\beta =-p$ and $\alpha \beta =q$

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

$={(-p)}^3-3q(-p)$

$={-p}^3+3pq$