Question

Form the quadratic equation with rational coefficients whose one of the root is $1-3\sqrt{5}$.

• A. $x^2-2x-44=0$
• B. $x^2+2x-44=0$
• C. $x^2-2x+44=0$
• D. $x^2+2x+44=0$

Answer 1

The correct option is A $x^2-2x-44=0$

If one of the roots of the equation is $1-3\sqrt{5}$ other will be $1+3\sqrt{5}$
Thus, sum of roots $=2$
Product of roots $=(1-3\sqrt{5})(1+3\sqrt{5})=1-9\times 5=-44$
Hence, the equation can be written as $x^2-Sx+P=0$
$\therefore x^2-2x-44=0$