SOLUTION: f(x)=2x^4-x^3-7x^2+4x-4 I am looking for all real zeroes.

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Question 1053299: f(x)=2x^4-x^3-7x^2+4x-4 I am looking for all real zeroes.
Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.
According to the rational root theorem, rational roots, if exist, must be among the numbers 1, -1, 2, -2.

Check them.

Do you know what to do next?



Plot y = 2x%5E4-x%5E3-7x%5E2%2B4x-4

Next you should divide your polynomial by  (x-2)*(x+2) = x%5E2-4  (based on the Remainder Theorem)  and analyse the quotient polynomial.

On the Rational Roots Theorem see  this  Wikipedia article.

On the Remainder Theorem see the lesson
    - Divisibility of polynomial f(x) by binomial x-a
in this site.

As your assistant, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this textbook under the topic "Remainder theorem".