Question

find the qudradic equation with roots 2+root 3 and 2-root3

Answer 1

Answer:

The answer is $x^2-4x+1=0$

Step-by-step explanation:

Given roots are $2+\sqrt 3$ and $2-\sqrt 3$

Thus

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

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

Therefore the required quadratic equation is

                  $x^2-\text{ (Sum of roots) } x+\text{(Product of roots)}=0$

                   $\Rightarrow x^2-4x+1=0$