Mathematics - Complex Number Question with Solution | TestHub

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. $\frac{\sqrt{2\sqrt{2}\pm \sqrt{(2\sqrt{2}{)}^2-4}}}{2}=\frac{2\sqrt{2}\pm 2}{2}=\sqrt{2}\pm 1$ this is irrational $\therefore$ the roots are real and different.