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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 4: Q. 100 (page 211)

Is $\frac{1}{3}$ a zero of localid="1646142357128" $f (x) = 2 x^{3} + 3 x^{2} - 6 x + 7$ ? Explain.

Short Answer

Expert verified

$\frac{1}{3}$ is not a zero of function $f (x) = 2 x^{3} + 3 x^{2} - 6 x + 7$ becouse $f (\frac{1}{3}) 鈮� 0$

Step by step solution

01

Step 1. Given data

The given function is

$f (x) = 2 x^{3} + 3 x^{2} - 6 x + 7$

Zero of the function is $\frac{1}{3}$

02

Step 2. Verification

Substitute $\frac{1}{3}$ for x in the function

role="math" $f (x) = 2 x^{3} + 3 x^{2} - 6 x + 7 f (\frac{1}{3}) = 2 {(\frac{1}{3})}^{3} + 3 {(\frac{1}{3})}^{2} - 6 (\frac{1}{3}) + 7 f (\frac{1}{3}) = \frac{2}{27} + \frac{1}{3} - 2 + 7 f (\frac{1}{3}) = 5.407$

$f (\frac{1}{3})$ is not equal to zero so $\frac{1}{3}$ is not a zero of the function

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