Question

Find the quadratic equation whose one of the root is $2+\sqrt{3}$.

Answer 1

For the quadratic equation if one root is $2+\sqrt{3}$

Other root is $2-\sqrt{3}$

Sum of roots$=2+\sqrt{3}+2-\sqrt{3}=4$

Product of roots$=(2+\sqrt{3})(2-\sqrt{3})=4-3=1$

$\therefore$Quadratic equation is $x^2-4x+1=0$