Question 733248: use the rational zero theorem and descartes’ rule of signs to assist you in finding all real and imaginary roots for x^4+2^3-3x^2-4x+4=0
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! (Assuming you mean the second term is 2x^3)
 , ___________ 2 sign changes. Expect 2 positive roots.
Let x become -x.
 ,_________ 2 sign changes. Expect 2 negative roots.
Choices for checking roots would be -1, -2, -4, +1, +2, +4.
Use of synthetic division shows -2 root, +2 NOT root, -1 NOT root, +1 root.
So far, Real roots seem to be -2 and +1.
The polynomial now rendered to check is  . Use of general solution to quadratic equation (even though this one is factorable) indicates roots -2 and +1. They occur in the factorization for the originally given degree 4 polynomial TWICE.
Roots are all REAL numbers, and are -2, +1, -2 (again), and +1 (again).
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