Question

Let us consider a quadratic equation $x^2+3ax+2a^2=0$
If this equation has roots $\alpha ,\beta$ and it is given that ${\alpha }^2+{\beta }^2=5$, then value of discriminant, $D$, for the above quadratic equation is

• A. $D>0$
• B. $D<0$
• C. $D=0$
• D. none of these

Answer 1

The correct option is A $D>0$

$A{x}^2+Bx+C=0$

Then $D=B^2-4AC$

In given equation

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

$A=1,B=3a$ and $C=2a^2$

Then,

$D=B^2-4AC$

So,

$(3a{)}^2-4(2a^2)=9a^2-8a^2=a^2$

Thus,

$a^2>0$

Then

$D>0$