For a polynomial (of degree 3 or 4) with real coefficients how can we determine the number of real positive roots?
or phrased a different way
What conditions enure that a polynomial (of degree 3 or 4) with real coefficients has 0,1,2,3,or 4 positive real roots?
I have a set of polynomials which have complicated coefficients which consists of several constants. I can determine the conditions when these coefficients are positive or negative. I am interested in only the positive real roots of these polynomials.
Possible Theorems to Use
- These posts with similar titles Number of real positive roots of a polynomial? Number of real positive roots of a polynomial? as the polynomials in these questions have numbers as their coefficients (rather than unknown constants) or have a specific structure.
- I am not interested in finding the explicit roots to these polynomials. I can solve them using Mathematica and other computer algebra systems. Determining when the roots are positive and real is the real problem.
- I am not sure what tags to use for this post, suggestions and edits are welcome.