Mathematics

Problem

Consider the quadratic equation

x^2+(k-3)x+2=0

. Which inequality on

k

guarantees that the equation has two distinct real roots? a)

k<3+2\sqrt{2}

3-2\sqrt{2}<k<3+2\sqrt{2}

k<3-2\sqrt{2}\;\text{or}\;k>3+2\sqrt{2}

k\le3-2\sqrt{2}\;\text{or}\;k\ge3+2\sqrt{2}