document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #589511 by Theo(13342) $\"\"$ $\"About$

You can put this solution on YOUR website!
this is fairly easy to construct if you know the trick.
\n" ); document.write( "you want a multiplicity of 2 for at least one of the zeroes.
\n" ); document.write( "we'll choose a multiplicity of 2 for the zero at x = 2
\n" ); document.write( "the factors would be (x-2) * (x-2)
\n" ); document.write( "we'll let the other 3 factors be 3, 4, and 5.
\n" ); document.write( "the factors are now (x-2) * (x-2) * (x-3) * (x-4) * (x-5).
\n" ); document.write( "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.
\n" ); document.write( "your equation will be:
\n" ); document.write( "y = (x-2)^2 * (x-3) * (x-4) * (x-5).
\n" ); document.write( "this is a fifth degree equation.
\n" ); document.write( "the simplified version will be:
\n" ); document.write( "y = x^5 - 16x^4 + 99x^3 - 296x^2 + 428x - 240
\n" ); document.write( "the graph of the equation is shown below.
\n" ); document.write( "both forms of the equation are graphed.
\n" ); document.write( "both forms are identical as shown by the fact that they both generate the same graph.
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