write a polynomial function of least degree with integral coefficients that has these given zeros: 1/5 mult. 2, -5
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The zeroes can be expressed as x=⅕, that is, x-⅕=0, 5x-1=0; and x=-5, that is, x+5=0. The multiplicity factor means that the factor is (5x-1)².

So, f(x)=(5x-1)²(x+5)=(25x²-10x+1)(x+5)=

25x³-10x²+    x+

        125x²-50x+5=25x³+115x²-49x+5.

This is one example of the required function. Multiplying this polynomial by a constant gives other examples.

by Top Rated User (711k points)

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