Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding - Page 112: 76

The two solutions are real (and not equal to each other).

$2x^{2}-4x+1=0$ To determine the nature of the solutions (without solving), we compute the sign of the discriminant in the quadratic formula ($a=2,\ b=-4,\ c=1$): $b^{2}-4ac=(-4)^{2}-4*2*1=16-8=8$ Since the discriminant is positive, the two solutions are real (and not equal to each other).