Question

The quadratic equation having the roots $(1+\sqrt{2})$ and $(1-\sqrt{2})$ is

• A. $x^2+2x+1=0$
• B. $x^2+2x-1=0$
• C. $x^2-2x-1=0$
• D. $x^2-2x+1=0$

Answer 1

The correct option is C $x^2-2x-1=0$

Roots of some quadratic equation are $(1+\sqrt{2})$ and $(1-\sqrt{2})$

$⟹$ $x=(1+\sqrt{2})orx=(1-\sqrt{2})$

$⟹$ $x-(1+\sqrt{2})=0orx-(1-\sqrt{2})=0$

$⟹$ $(x-(1+\sqrt{2}\left)\right)(x-(1-\sqrt{2}\left)\right)=0$

$⟹$ $x^2-x+x\sqrt{2}-x-x\sqrt{2}+1-2=0$

$⟹$ $x^2-2x-1=0$

Hence, option $C$ is correct.