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  4. The quadratic equation with rational coefficient whose one root is (1/2+√5), is

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Q. The quadratic equation with rational coefficient whose one root is $\frac{1}{2+\sqrt{5}}$, is

Complex Numbers and Quadratic Equations

Solution:

$ \alpha=\frac{1}{2+\sqrt{5}}=\sqrt{5}-2$
$ \beta=-\sqrt{5}-2$
$ \alpha+\beta=-4, \alpha \beta=-1$
so quadratic equation is
$x^2+4 x-1=0$