Question

Form the quadratic equation with rational coefficients whose one of the root is:

$\sqrt{7}-\sqrt{2}$

• A. $y^2-\sqrt{7}y+5=0$
• B. $y^2+2\sqrt{7}y+5=0$
• C. $y^2-2\sqrt{7}y-5=0$
• D. Equation with rational coefficients is not possible.

Answer 1

The correct option is D Equation with rational coefficients is not possible.

If one of the roots of the equation is $\sqrt{7}+\sqrt{2}$ other will be $\sqrt{7}-\sqrt{2}$
Thus, sum of roots $=2\sqrt{7}$
Product of roots $=(\sqrt{7}+\sqrt{2})(\sqrt{7}-\sqrt{2})$ = $7-2=5$
Hence, the equation can be written as $x^2-Sx+P=0$
$\therefore x^2-2\sqrt{7}x+5=0$