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

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

Step by step solution

Given information

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

Determine the all possible zero of the given function.

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

$p = \pm 1, \pm 3$

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

$q = \pm 1, \pm 2, \pm 3, \pm 4 \pm 6, \pm 12$

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

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

Write the conclusion

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

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

Short Answer

Step by step solution

Given information

Determine the all possible zero of the given function.

Write the conclusion

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List all the potential rational zeros of f(x)=12x8-x7+6x4-x3+x-3.

Short Answer

Step by step solution

Given information

Determine the all possible zero of the given function.

Write the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Statistics

Mechanics Maths

Pure Maths

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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