Question

$x^2+3ax+2a^2=0$
If the above equation has roots $\alpha ,\beta$ and it is given that ${\alpha }^2+{\beta }^2=5$, then the product of roots is

• A. $2$
• B. $1$
• C. $-3$
• D. $3$

Answer 1

Answer: (A)

$2$

$\alpha +\beta =-3a$
$\alpha \beta =2a^2$
${\alpha }^2+{\beta }^2=5$
$(\alpha +\beta {)}^2-2\alpha \beta =5$
$9a^2-2\left(2a^2\right)=5$
$5a^2=5$
$a=\pm 1$
Product of the roots, $\alpha \beta =2a^2=2\left(1\right)=2$