Question

If one of the roots of the quadratic equation is $(2+\sqrt{3})$ then the quadratic equation is

• A. $x^2-(2+\sqrt{3})x+1=0$
• B. $x^2+(2+\sqrt{3})x+1=0$
• C. $x^2-4x+1=0$
• D. $x^2+4x-1=0$

Answer 1

The correct option is C $x^2-4x+1=0$

When one root of the quadratic equation are irrational then both the roots are conjugate pairs
$\therefore$ Other roots of quadratic equation $=2-\sqrt{3}$ Sum of the roots = $(2+\sqrt{3})+(2-\sqrt{3})=4$
Product of roots = $(2+\sqrt{3})(2-\sqrt{3})=1$

$\therefore$ Quadratic equation
$x^2$ - (sum of roots)$x$ + product of roots = 0

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