Question

If $\alpha ,\beta$ are the roots of $x^2$ + 12x + 50, then ${\alpha }^2\beta +{\beta }^2\alpha$ is equal to

• A. 60
• B. 12
• C. -60
• D. 5

Answer 1

The correct option is C -60

Given that, $\alpha$ & $\beta$ are the roots of the equation. $x^2$ + 12x + 5 = 0
Sum of the roots = $\alpha +\beta =\frac{-b}{a}=\frac{-12}{1}=-12$
Product Of the roots = $\alpha \beta =\frac{c}{d}=\frac{5}{1}=5$
${\alpha }^2\beta +{\beta }^2\alpha =\alpha \beta (\alpha +\beta )=-12\times 5=-60$