Question

The roots of the equation $x^2-2\sqrt{2}x+1=0$ are

• A. Real and different
• B. Imaginary and different
• C. Real and equal
• D. Rational and different

Answer 1

Answer: (A)

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