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  4. If one root of a quadratic equation with rational coefficients is √3+2, then the quadratic equation is

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Q. If one root of a quadratic equation with rational coefficients is $\sqrt{3}+2$, then the quadratic equation is

Complex Numbers and Quadratic Equations

Solution:

$ \alpha=\sqrt{3}+2 $
$b =-\sqrt{3}+2 $
$P =\alpha \beta=1$
$S =\alpha+\beta=4 $
$\Rightarrow \text { quadratic equation is } x ^2-4 x +1=0 $