Answer: $\mathbf C$
Explanation:
For the given equation::
Let $\alpha$ and $\beta$ be the roots.
Now, sum of roots = $\alpha + \beta = \frac{-b}{a} = -3 \tag{1}$
product of roots = $\alpha\beta = \frac{c}{a} = 4 \tag{2}$
Now,
We need to find the equation having roots $(\alpha + \beta)^2$ and $(\alpha - \beta)^2$.
So, for this equation:
Sum of roots = $(\alpha + \beta)^2 \bf{+} (\alpha - \beta)^2 \implies 2(\alpha^2 + \beta^2)\implies 2[(\alpha + \beta)^2-2\alpha\beta]\tag{3}$
From equations, $\mathbf {1, 2, and\; 3}$, we get:
$\implies 2[(\alpha + \beta)^2-2\alpha\beta]\implies2[(-3)^2-2*4] = 2[9-8] = 2$
So, sum of roots coming out = $2$
Now, check the options and find the sum of their roots
For $A$ option, it is $-2$ and same for other options
For $C$ option, it is $2$
$\therefore \mathbf C$ is the correct option.