College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.9 - Solving Equations and Inequalities Graphically - 1.9 Exercises: 19

Answer

The solutions are $x=\left\{1, 2, 3\right\}$.

Work Step by Step

To solve the given equation graphically, perform the following steps: (1) Graph the function $y=x^3-6x^2+11x-6$ using a graphing utility. Refer to the image below for the graph. (2) Identify the point/s where the graph touch/cross the x-axis. These are the points where the value of $x^3-6x^2+11x-6$ is zero. The x-coordinates of these points are the solutions to the given equation. Notice that the graph crosses the x-axis at $(1, 0)$, $(2, 0)$, and $(3, 0)$. This means that the solutions to the given equation are $1, 2, $ and $3$. Thus, the solutions are $x=\left\{1, 2, 3\right\}$.
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