Find rational roots of x^4 - 4x^3 + 2x^2 + 4x + 4

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vikramtiwari

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I need help in figuring out the roots of this weird looking polynomial...

Q1) Consider the polynomial...P(x) = x^4 - 4x^3 + 2x^2 + 4x + 4
Find all the Rational Roots of this polynomial...?
 
Re: polynomials...

Is there a typo? No rational roots for what you have typed, unless I'm missing something.
 
Not only it does not have any rational root - it does not have any real roots.
 
I have a feeling that the instructions were actually something like "Use the Rational Roots Test to list any possible rational zeroes".

(Educators are discovering that, having told their students for years that "real math" comes from their calculators, the kids are now just copying presumed roots from the pretty pictures on the screens of their graphing calculators. The only way to "force" a student to use the mathematics in this case would be to provide a polynomial that doesn't actually have any zeroes which can be copied from the picture.)

Just my opinion, of course; I could be wrong.... :wink:

Eliz.
 
I thought there was a typo too...but when I explore the web pages...it mentions something about Rational Root Theorem! and with the help of it they solve such a weird looking polynomials...Apart from that, if that helps we may use the Descarte's Rule of signs, we may find all the positive and negative real roots...
So, there are at most 2 positive and at most 2 negative roots.

Please help, if anyone knows how to resolve it!

Thanks a lot !
 
vikramtiwari said:
Please help, if anyone knows how to resolve it!
Click to expand...
The first reply should have "resolved" this question, as it clearly stated that there are no rational zeroes for this polynomial. But since this did not answer your question, it might help if you replied with clarification, perhaps also including answers to the various questions and issues raised by the other posters to this thread.

Please be complete. Thank you! :D

Eliz.
 
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