Question

If $2+\sqrt{3}$is a root of the equation $x^2+px+q=0$, then write the values of p and q.

Answer 1

Since, a root of the equation $x^2+px+q=0$ ...(i) If $2+\sqrt{3}$ in one of the solution (root) of (i) in $2-\sqrt{3}$ will be other roots Now, sum of roots = $\frac{-b}{a}\Rightarrow (2+\sqrt{3})+(2-\sqrt{3})=-p\Rightarrow 4=-pandproductofroot=\frac{c}{a}\Rightarrow (2+\sqrt{3})(2-\sqrt{3})=2\Rightarrow 4-3=q\Rightarrow q=1Thus,p=-4,q=1$