Question

If one zero of the quadratic polynomial $x^2+px+4$ is 2, the other zero is $\alpha$. Find the value of $-p\alpha$.

Answer 1

$x^2+px+4=0$

$\alpha \beta =4$

$⟹2\alpha =4$

So, $\alpha =2$

$⟹\beta =2$

$\alpha +\beta =-p$

$⟹p=-4$

$\therefore -p\times \alpha =4\times 2=8$