Question

Form a quadratic equation whose roots are $7\pm 2\sqrt{5}$.

Answer 1

Sum of roots $=7+2\sqrt{5}+7-2\sqrt{5}=14$

Product of roots $=(7+2\sqrt{5})(7-2\sqrt{5})=49-20=29$

Required equation,

$x^2-$ (sum of roots) $x+$product of roots$=0$

$⟹x^2-14x+29=0$