Finding roots of polynomials

Looks like an extension of this thread: http://www.excelforum.com/excel-gene...ial-roots.html

Short but useless answer, yes there are several different ways to code -- whether in VBA or with Excel worksheet formulas -- the roots of a polynomial.

1) If your polynomial will always be 4th degree or less, and you are willing to venture into the realm of complex numbers, there are formulas (similar to the quadratic formula that you learned in your secondary level algebra classes). These formulas, though they exist, tend to be quite complex, so it is not always desirable to use them.
http://en.wikipedia.org/wiki/Quartic_function
http://en.wikipedia.org/wiki/Cubic_function

2) As noted in the other thread, one can readily use Solver or Goal seek to find the roots of polynomials. These methods can be automated through VBA, and we have many examples on this site.

3) My personal preference with polynomials, is to code a numeric root finding algorithm (Newton Raphson, bisection, or false position, depending on my mood that day) into a User Defined function. With simple polynomials, I personally find it easier to code my own algorithm than to coax Solver to run from VBA. A UDF also has the advantage of being flexible enough to call from any worksheet cell. Since it can be used like any other Excel function, it naturally fits into automated spreadsheet calculations.

How would you prefer to proceed?

If you are unfamiliar with them, you will need to be aware of Excel's built in complex number functions (such as IMSQRT(), IMPOWER(), etc.). I am not real familiar with the solutions for the cubic and quartic equations, but, at least the cubic solution, will require complex numbers as part of the computation, and you will need these Excel functions to compute the complex numbers. See a list of IM...() functions here: https://support.office.com/en-US/art...rs=en-US&ad=US