Question

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

Answer 1

Given that the roots of equation are $2+\sqrt{3},2-\sqrt{3}$

Let the quadratic equation whose roots are $2+\sqrt{3},2-\sqrt{3}$ be $x^2+bx+c=0$

We know that, sum of the roots is $-b$

$\Rightarrow -b=2+\sqrt{3}+2-\sqrt{3}=4$

$\Rightarrow b=-4$

We know that the product of the roots is $c$

$\Rightarrow c=(2+\sqrt{3})\times (2-\sqrt{3})=4-3=1$

So the equation is $x^2-4x+1=0$