Question

Form the quadratic equation with rational coefficient, if its one of the root is$\sqrt{5}-\sqrt{3}$, then the equation is

• A. $x^2\pm 6x+6=0$
• B. $x^2\pm 7x+6=0$
• C. $x^2\pm 7x+16=0$
• D. none of the above

Answer 1

The correct option is D none of the above

If one root is $\sqrt{5}-\sqrt{3}$ then the other root will be $\sqrt{5}+\sqrt{3}$
Sum of root = $2\sqrt{5}$
Product of roots = $(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})$ = 5 - 3 = 2
The equation whose standard form is $x^2-Sx+P=0$ will be, $x^2-2\sqrt{5}x-2=0$