Question

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

$\sqrt{3}-\sqrt{7}$

• A. $y^2-2\sqrt{3}y-4=0$
• B. $y^2+2\sqrt{3}y-4=0$
• C. $y^2-2\sqrt{3}y+4=0$
• D. Equation with rational coefficient is not possible

Answer 1

The correct option is D Equation with rational coefficient is not possible

If one of the roots of the equation is $\sqrt{3}-\sqrt{7}$ other will be $\sqrt{3}+\sqrt{7}$
Thus, sum of roots $=2\sqrt{3}$
Product of roots $=(\sqrt{3}-\sqrt{7})(\sqrt{3}+\sqrt{7})$ = $3-7\times 5=-4$
Hence, the equation can be written as $x^2-Sx+P=0$
$\therefore x^2-2\sqrt{3}x-4=0$