Question

Form the quadratic equation whose roots are $7+\sqrt{3}$ and $7-\sqrt{3}$.

Answer 1

The roots are $7+\sqrt{3},7-\sqrt{3}$
Sum of the roots $=7+\sqrt{3}+7-\sqrt{3}=14$
Product of roots $=(7+\sqrt{3})(7-\sqrt{3})=49-3=46$
The required equation is
$x^2-$ (Sum of the roots) $x$ $+$ Product of roots $=0$
$x^2-14x+46=0$