SOLUTION: what does descrates rule of signs tell me about number of real positive zeros and negative real zeros of this function. 5x raised to the 6th-3x raised to the 3rd+x squared-x?

Question 433594: what does descrates rule of signs tell me about number of real positive zeros and negative real zeros of this function. 5x raised to the 6th-3x raised to the 3rd+x squared-x?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Descartes' rule of signs only gives insight on whether a root is positive or negative, not whether a root is zero.
The polynomial has a root of 0. Thus apply Descartes' rule only on . Hence, there might 3 positive roots or 1 positive root. (3 variation of signs.)
Considering , (replacing x by -x), we see that there are no negative roots. (No variation of signs.)
Hence the original polynomial have 0 as a root, 3 positive roots, and 2 complex roots,
OR
have 0 as a root, 1 positive root, and 4 complex roots.
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