Question 1023589: Please help me I am so lost. Please show all steps and work. Thanks
Real Zeros of Polynomials
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).
P(x)=
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Real Zeros of Polynomials
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).
P(x)= x*x*(x-3)*(x-3)*(x+4)
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! 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.
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.
http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/index.htm
all the tutorials are good, but the ones that refrerence zeroes of polynomials in particular are tutorials 38 and 39.
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