College Algebra Help

[guardgirl08]

Im working on homework and came across a problem that is really complicated.

Use the Function g(x)=x^5 -3x^4 -24x^3 +72x -240 to find all the zeros of g(x) and state each multiplicity.

So far I found the factors of p & q or 1 & -240 but when I went to plug the numbers in and do the synthetic division, none of them worked.

 

[mmm4444bot]

when I [did] … the synthetic [divisions], none of them worked.

You should have been told that this result means none of the zeros are rational.

You posted the instruction (in part) as "find all the zeros". Please check the instructions to see if they specify all Real zeros.

Will you also confirm that there is no x^2 term in the given polynomial? In fact, please proofread the entire polynomial, in your post.

A fifth-degree polynomial defines function g. This means that it has five zeros. It turns out that four of them are Complex numbers with an imaginary part, and only one is Real. This is why I find it odd that they ask for the multiplicity of each.

Were you expecting imaginary numbers, in some of your exercises? If not, then perhaps your materials contain a typographical error. (For example, if the term 77x^2 were present, synthetic division would show that x = 4 is a zero.)

I would need to use a machine, were I to find decimal approximates for all of the zeros in this exercise as posted. Here is a graph of the interesting part of y = g(x). Note that there is only one x-intercept.

[attachment=0:34crjsxs]non-rational.JPG[/attachment:34crjsxs]

 

[guardgirl08]

This is what the question is...I am copying it word for word from my paper.

Use the function g(x)=x^5 -3x^4 -24x^3 +72x -240
a)find all the zeros of g(x) and state each multiplicity
b)find all the x and y intercepts
c)Draw the number line to determine when the graph is above and below the x-axis
d)Determine the end behavior
e)using a-d graph g(x)

This is what the entire question is.

 

[mmm4444bot]

Were you expecting imaginary numbers, in some of your exercises? If not, then perhaps your materials contain a typographical error.

 

[mmm4444bot]

word for word from my paper

Use the function g(x)=x^5 -3x^4 -24x^3 +72x -240

a)find all the zeros of g(x) and state each multiplicity Again, you need a computer for this

b)find all the x and y intercepts Ditto, for calculating the single x-intercept

The y-intercept is obvious to you, yes?

c)Draw the number line to determine when the graph is above and below the x-axis

This would be inequality tests, using the zeros and factors of g(x) to make a sign chart underneath the Real number line, followed by analysis of the sign of the "product" of the factors' signs, I think

d)Determine the end behavior This can be done without a computer; it involves thinking about the leading coefficient, yes?

e)using a-d graph g(x) I would use a computer here, too.

Or not. If you're paying attention to me, then you already realize that you have this graph!

If you are convinced that you should not need a computer for this exercise, then your paper contains a typographical error.

Here is my best guess at what the polynomial is supposed to be:

g(x) = x^5 - 3x^4 - 24x^3 + 72x^2 - 40x

Note that I changed the character string "+ 72x - 240" to "+ 72x^2 - 40x". In other words, I'm sensing that the mistake is that the exponent on x^2 somehow slide to the right, appending itself in front of the -40 to make -240, and both powers of x were subsequently reduced by 1.

:idea: This new and improved version of g(x) has all Real zeros (one of which is obvious to you, by inspection, yes?), and three of the zeros are Integers, so it's a perfect poly to replace the pitiable, poorly-programmed poly in this exercise. Go for it!

By the way, is this an on-line course? Did you print your paper from the Internet? I would like to know, if you don't mind sharing.

You can print out this thread, give it to your instructor, and inform them that my fee for proofreading and correcting their course materials is $20. :wink:

Please feel free to come back and post specific questions about this exercise, after you use synthetic division and quadratic methods to find all zeros.

Cheers ~ Mark