Learning Materials
Features
Discover
Chapter 3: Problem 79
Find the rational zeros of the polynomial function. $$f(x)=x^{3}-\frac{1}{4} x^{2}-x+\frac{1}{4}=\frac{1}{4}\left(4 x^{3}-x^{2}-4 x+1\right)$$
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
A graph of \(y=f(x)\) is shown, where \(f(x)=2 x^{5}-3 x^{4}+x^{3}-8 x^{2}+5 x+3\) and \(f(-x)=-2 x^{5}-3 x^{4}-x^{3}-8 x^{2}-5 x+3\). (a) How many negative real zeros does \(f\) have? Explain. (b) How many positive real zeros are possible for \(f ?\) Explain. What does this tell you about the eventual right-hand behavior of the graph? (c) Is \(x=-\frac{1}{3}\) a possible rational zero of \(f ?\) Explain. (d) Explain how to check whether \(\left(x-\frac{3}{2}\right)\) is a factor of \(f\) and whether \(x=\frac{3}{2}\) is an upper bound for the real zeros of \(f\).
Determine algebraically any point(s) of intersection of the graphs of the equations. Verify your results using the intersect feature of a graphing utility. $$\begin{aligned} &y=9-x^{2}\\\ &y=x+3 \end{aligned}$$
Find all real zeros of the polynomial function. $$g(x)=4 x^{5}+8 x^{4}-15 x^{3}-23 x^{2}+11 x+15$$
Use the zero or root feature of a graphing utility to approximate (accurate to the nearest thousandth) the zeros of the function, (b) determine one of the exact zeros and use synthetic division to verify your result, and (c) factor the polynomial completely. $$f(s)=s^{3}-12 s^{2}+40 s-24$$
Find the zeros (if any) of the rational function. Use a graphing utility to verify your answer. $$f(x)=\frac{x^{2}+4 x-21}{x^{2}-4 x+3}$$
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine