Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.5 - Zeros of Polynomial Functions - Exercise Set - Page 379: 69


A polynomial equation with real coefficients of degree 3 must have at least one real root.

Work Step by Step

According to the Fundamental Theorem of Algebra, a ${{n}^{th}}$ degree polynomial has exactly $n$ roots. Also, if $f\left( x \right)$ is a polynomial with real coefficients and $x=a+ib$ is a solution of $f\left( x \right)=0$ then $x=a-ib$ is also a solution of $f\left( x \right)=0$. Hence, we can say that a cubic equation can have one real root and two complex roots or it can have three real roots Therefore, a cubic equation must have at least one real root.
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