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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. 101 (page 211)

Is $\frac{3}{5}$ a zero of localid="1646143732762" $f (x) = 2 x^{6} - 5 x^{4} + x^{3} - x + 1$ ? Explain.

Short Answer

Expert verified

$\frac{3}{5}$ is not a zero of function $f (x) = 2 x^{6} - 5 x^{4} + x^{3} - x + 1$ becouse $f (\frac{3}{5}) 鈮� 0$

Step by step solution

01

Step 1. Given data

The given function is

$f (x) = 2 x^{6} - 5 x^{4} + x^{3} - x + 1$

Zero of the function is $\frac{3}{5}$

02

Step 2. Verification

Substitute $\frac{3}{5}$ for x in the function

localid="1646143682252" $f (x) = 2 x^{6} - 5 x^{4} + x^{3} - x + 1 f (\frac{3}{5}) = 2 {(\frac{3}{5})}^{6} - 5 {(\frac{3}{5})}^{4} + {(\frac{3}{5})}^{3} - (\frac{3}{5}) + 1 f (\frac{3}{5}) = 0.06 f (\frac{3}{5}) 鈮� 0$

$f (\frac{3}{5})$ is not equal to zero so $\frac{3}{5}$ is not a zero of the function

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Most popular questions from this chapter

In Problems 21鈥�32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

$f (x) = - 4 x^{3} - x^{2} + x + 2$

Solve the inequality algebraically.

$x^{4} < 9 x^{2}$

Analyze each polynomial function using Steps $1$ through $8$ :

$f (x) = x^{4} + x^{3} - 3 x^{2} - x + 2$ .

True or False The graph of a rational function may intersect a vertical asymptote.

Find the domain of the rational function.

$F (x) = \frac{3 x (x - 1)}{2 x^{2} - 5 x - 3}$

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