Question 1023589
The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=3 and x=0, and a root of multiplicity 1 at x=−4
Find a possible formula for P(x).


with roots at x = 3 and x = 0 and x = -4, your possible factors are:


(x-3) * x * (x+4)


the roots at x = 3 and x = 0 have roots of multiplicity 2.


this means the same root occurs 2 times.


therefore, your possible factors become:


(x-3)^2 * x^2 * (x+4)


if you multiply all these factors together, you get a possible formula for p(x).


when you multiply the factors together, your equation becomes p(x) = x^5 - 2x^4 - 15x^3 + 36x.


the graph of that equation is shown below.


<img src = "http://theo.x10hosting.com/2016/030601.jpg" alt="$$$" </>


if the multiplicity is even, then the graph touches the x-axis but doesn't cross it.


if the multiplicity is odd, then the graph crosses the x-axis.


here's a good reference that will help you a lot if you take the time to read it.


<a href = "http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/index.htm" target = "_blank">http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/index.htm</a>


all the tutorials are good, but the ones that refrerence zeroes of polynomials in particular are tutorials 38 and 39.