Question

The roots of the quadratic equation are $(1+\sqrt{2})$ and $(1-\sqrt{2})$. Form the quadratic equation.

Answer 1

Sum of roots $=1+\sqrt{2}+1-\sqrt{2}$

$=2$

Product of roots $=(1+\sqrt{2})(1-\sqrt{2})$

$=1-2$

$=-1$

Equation $\Rightarrow x^2-\left(sumofroots\right)x+\left(productofroots\right)$

$\Rightarrow x^2-2x-1$