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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. 15 (page 245)

List all the potential rational zeros of $f (x) = 12 x^{8} - x^{7} + 6 x^{4} - x^{3} + x - 3$ .

Short Answer

Expert verified

$\frac{p}{q} = 卤 1, 卤 3, 卤 \frac{1}{2}, 卤 \frac{3}{2}, 卤 \frac{1}{3}, 卤 \frac{1}{4}, 卤 \frac{3}{4}, 卤 \frac{1}{6}, 卤 \frac{1}{12}$

Step by step solution

01

Given information

The given polynomial function is $f (x) = 12 x^{8} - x^{7} + 6 x^{4} - x^{3} + x - 3$

02

Determine the all possible zero of the given function.

List all the possible factors $p$ of $a_{0}$ .

$p = 卤 1, 卤 3$

List all the possible factors $q$ of $a_{8}$ .

$q = 卤 1, 卤 2, 卤 3, 卤 4 卤 6, 卤 12$

Identify all possible rational zeros $\frac{p}{q}$ .

$\frac{p}{q} = 卤 1, 卤 3, 卤 \frac{1}{2}, 卤 \frac{3}{2}, 卤 \frac{1}{3}, 卤 \frac{1}{4}, 卤 \frac{3}{4}, 卤 \frac{1}{6}, 卤 \frac{1}{12}$

03

Write the conclusion

The possible real zeros are $卤 1, 卤 3, 卤 \frac{1}{2}, 卤 \frac{3}{2}, 卤 \frac{1}{3}, 卤 \frac{1}{4}, 卤 \frac{3}{4}, 卤 \frac{1}{6}, 卤 \frac{1}{12}$ .

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Most popular questions from this chapter

In Problems 39鈥�56, find the real zeros of f. Use the real zeros to factor f.

$f (x) = 2 x^{4} - 3 x^{3} - 21 x^{2} - 2 x + 24$

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See all solutions

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