Question

Form the quadratic equation whose roots are $3+2\sqrt{5}$ and $3-2\sqrt{5}$

Answer 1

Let 'm' and 'n' be the roots $\therefore m=3+2\sqrt{5}$ and $n=3-2\sqrt{5}$
Sum of the roots $=m+n=3+2\sqrt{5}+3-2\sqrt{5}\therefore m+n=6$
Product of the roots $=mn=(3+2\sqrt{5})(3-2\sqrt{5})=(3{)}^2-(2\sqrt{5}{)}^2=9-20\therefore mn=-11$
$x^2-(m+n)x+mn=0\therefore x^2-6x-11=0$