document.write( "Question 1052680: I am having trouble with determining the polynomial function for the problem of two zeros, one is 2 with multiplicity 1 and the other is 1 with multiplicity 3. The polynomial is of the fourth degree and and is asking for the leading coefficient to be 1. \r
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Algebra.Com's Answer #668010 by htmentor(1343) $\"\"$ $\"About$

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The multiplicity is determined by the exponent of the factor that produced the root. So the factor for the multiplicity 1 root will be a first order polynomial and the multiplicity 3 root will have a third order polynomial. We are given the two roots and we must have the leading coefficient equal to 1, so we can factor the polynomial in the following way: (x-1)^3(x-2) = 0. This can be further written as (x-1)(x-1)(x-1)(x-2), which makes it easy to see the multiplicity. Setting this equal to zero we see that this gives the correct roots, 1 (mult. 3) and 2 (mult. 1).
\n" ); document.write( "Carrying out the multiplication gives f(x)= x^4-5x^3+9x^2-7x+2\r
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