Consider the quadratic equation

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

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}

(b)

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

(c)

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

(d)

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