Solve the following


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


Irrational roots always occur in conjugate pairs.

If $2+\sqrt{3}$ is a root and $2-\sqrt{3}$ is its conjugate root.


$\Rightarrow 4=-9$

$\Rightarrow p=-4$

Also, $(2+\sqrt{3})(2-\sqrt{3})=q$

$\Rightarrow 4-3=q$

$\Rightarrow q=1$

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