If  $\frac{\alpha }{\alpha +1}$ and $\frac{\beta }{\beta +1}$ are the roots of the quadratic equation $x^2+7x+3=0$, then the equation having roots $\mathbf{\alpha }$ and  $\mathbf{\beta }$ is

$\frac{\alpha }{\alpha +1} is a root of x^2+7x+3=0$

$\frac{{\alpha }^2}{{\left(1+\alpha \right)}^2}+7\left(\frac{\alpha }{1+\alpha }\right)+3=0$

${\alpha }^2+7\alpha \left(1+\alpha \right)+3{\left(1+\alpha \right)}^2=0$

$11{\alpha }^2+13\alpha +3=0$

similarly $11{\beta }^2+13\beta +3=0$

$\alpha ,\beta are roots of 11x^2+13x+3=0$