Question

lf $\alpha +\beta =-2$ and ${\alpha }^3+{\beta }^3=-56$, then the quadratic equation whose roots are $\alpha ,\beta$, is:

• A. $x^2+2x-16=0$
• B. $x^2+2x-15=0$
• C. $x^2+2x-12=0$
• D. $x^2+2x-8=0$

Answer 1

Answer: (D)

$x^2+2x-8=0$

Given, $(\alpha +\beta )=-2$, ${\alpha }^3+{\beta }^3=-56$
$\Rightarrow (\alpha +\beta )({\alpha }^2+{\beta }^2-\alpha \beta )=-56$
$\Rightarrow (\alpha +\beta {)}^2-3\alpha \beta =28$
$\Rightarrow 4-3\alpha \beta =28$
$\Rightarrow \alpha \beta =-8$
$\Rightarrow x^2-(\alpha +\beta )x+\alpha \beta =0$
$\Rightarrow x^2+2x-8=0$