Explanation

(d)
Given, $\alpha,\ \beta$ are the roots of equation $x^{2} + 4x + 3 = 0$
$\therefore\ \ \alpha + \beta = - 4$ and $\alpha\beta = 3$
Now, $2\alpha + \beta + \alpha + 2\beta = 3(\alpha + \beta) = - 12$
And $(2\alpha + \beta)(\alpha + 2\beta) = 2\alpha^{2} + 4\alpha\beta + \alpha\beta + 2\beta^{2}$
$= 2(\alpha + \beta)^{2} + \alpha\beta$
$= 2( - 4)^{2} + 3 = 35$
Hence, required equation is
$x^{2} -$(sum of roots)$x +$(product of roots)=0
$\Rightarrow \ \ \ \ x^{2} + 12x + 35 = 0$