If the equations $x^3+5x^2+px+q=0$ and $x^3+7x^2+px+r=0$ have two roots in common, then the product of two non-common roots of two equations, is

Let $\alpha$ be a common root of the given equations. Then, 

   ${\alpha }^3+5{\alpha }^2+p\alpha +q=0$ and ${\alpha }^3+7{\alpha }^2+p\alpha +r=0$

$\therefore 2{\alpha }^2+q-r=0$

$\Rightarrow$Common roots are roots of the equation $2x^2+q-r=0$.

Clearly, sum of the common roots is zero. 

Let $\beta$ and $\gamma$ be the third roots of first and second equations respectively. Then,

$\beta =-5,\gamma =-7 [\because$Sum of the roots in two equations is zero$]$

$\Rightarrow \beta \gamma =35.$