Question

If $\alpha ,\beta$ are the roots of the equation $x^2+3x+2=0$. Then ${\alpha }^5+{\beta }^5=?$

• A. $33$
• B. $-32$
• C. $35$
• D. $-33$

Answer 1

Answer: (D)

$-33$

$x^2+3x+2=0$

$\Rightarrow$ $x^2+2x+x+2=0$

$\Rightarrow$ $x(x+2)+1(x+2)=0$

$\Rightarrow$ $(x+2)(x+1)=0$

$\Rightarrow$ $x+2=0$ and $x+1=0$

$\therefore$ $x=-2$ and $x=-1$

$\therefore$ $\alpha =-2$ and $\beta =-1$

$\Rightarrow$ $(\alpha {)}^5+(\beta {)}^5=(-2{)}^5+(-1{)}^5$

$=-32-1$

$=-33$

$\therefore$ $(\alpha {)}^5+(\beta {)}^5=-33$