Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.2 Linear and Quadratic Functions - Exercises - Page 19: 47


real solutions: $c \in (- \infty, -2] \cup [2, \infty)$

Work Step by Step

The equation $x^2 +cx+1$ has real roots if the discriminant $(c^2 - 4) \ge 0$ from the general law for solving a polynomial of second degree. Thus, we need to have: $|c| \ge 2$ which can be written as $c \in (- \infty, -2] \cup [2, \infty)$ Thus, any value in these intervals gives us a real solution. But any value of $c$ in the interval $(-2,2)$ gives us an imaginary (non-real) solution.
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