The sum and product of zeros of the quadratic polynomial are - 5 and 3 respectively the quadratic polynomial is equal to

If $\alpha$, $\beta$  be the zeros of the quadratic polynomial ,then
$\left(x-\alpha \right)\left(x-\beta \right)$ is the quadratic polynomial.
Thus, $\left(x-\alpha \right)\left(x-\beta \right)$ is the polynomial.
$=x^2-\alpha x-\beta x+\alpha \beta$
$=x^2-x\left(\alpha +\beta \right)+\alpha \beta (i)$ 
$\left(\alpha +\beta \right)=-5\alpha \beta =3$
Now putting the value of $\left(\alpha +\beta \right),\alpha \beta$ in equation (i) we get,
$x^2-x\left(-5\right)+3$
$=x^2+5x+3$