Question 964676: Give an example of a polynomial of degree 5 with three distinct zeros and multiplicity of 2 for at least one of the zeros. Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! this is fairly easy to construct if you know the trick.
you want a multiplicity of 2 for at least one of the zeroes.
we'll choose a multiplicity of 2 for the zero at x = 2
the factors would be (x-2) * (x-2)
we'll let the other 3 factors be 3, 4, and 5.
the factors are now (x-2) * (x-2) * (x-3) * (x-4) * (x-5).
multiply all these factors together and you should get a fifth degree equation with zeroes at 2,3,4,5 and a multiplicity of 2 for the zero at x = 2.
your equation will be:
y = (x-2)^2 * (x-3) * (x-4) * (x-5).
this is a fifth degree equation.
the simplified version will be:
y = x^5 - 16x^4 + 99x^3 - 296x^2 + 428x - 240
the graph of the equation is shown below.
both forms of the equation are graphed.
both forms are identical as shown by the fact that they both generate the same graph.
