College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding - Page 112: 75


The two solutions are complex conjugates.

Work Step by Step

$3x^{2}-3x+4=0$ To determine the nature of the solutions (without solving), we compute the sign of the discriminant in the quadratic formula ($a=3,\ b=-3,\ c=4$): $b^{2}-4ac=(-3)^{2}-4*3*4=9-48=-39$ Since the discriminant is negative, the two solutions are complex conjugates.
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