Question

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

$4\sqrt{2}-\sqrt{3}$

• A. $y^2-8\sqrt{2}y+23=0$
• B. $y^2+8\sqrt{2}y+23=0$
• C. $y^2-8\sqrt{2}y-23=0$
• 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 $4\sqrt{2}-\sqrt{3}$ other will be $4\sqrt{2}+\sqrt{3}$
Thus, sum of roots $=8\sqrt{2}$
Product of roots $=(4\sqrt{2}-\sqrt{3})(4\sqrt{2}+\sqrt{3})$ = $32-3=29$
Hence, the equation can be written as $x^2-Sx+P=0$
$\therefore x^2-8\sqrt{2}x+29=0$