The discriminant of the equation
$(-2 \sqrt{2})^{2}-4(1)(1)=8-4=4 >0$
and a perfect square, so roots are real and different but we can't say that roots are rational because coefficients are not rational therefore.
$\frac{\sqrt{2 \sqrt{2}+\sqrt{(2 \sqrt{2})^{2}-4}}}{2}$
$=\frac{2 \sqrt{2} \pm 2}{2}=\sqrt{2} \pm 1$
this is irrational
$\therefore $ the roots are real an different