Question

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

• A. $x^2-4x-1=0$
• B. $\sqrt{2}{x}^2-4x+1=0$
• C. $x^2+4x-1=0$
• D. $x^2+4x+1=0$

Answer 1

Answer: (C)

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