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Find a polynomial f(x) of degree 5 such that 1,-2, and 5 are roots; where 1 is a...

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Find a polynomial f(x) of degree 5 such that 1,-2, and 5 are roots; where 1 is a multiplicity of 3.

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We are given that the zeros of the function are 1,-2, and 5 where 1 has a multiplicity of 3.

 

If k is a root (zero, solution) for a function f(x), then (x-k) is a factor of f(x). Thus (x-1),(x+2) and (x-5) are all factors. Since the root 1 has multiplicity 3, the factor (x-1) occurs three times.

 

The required function is `f(x)=(x-1)^3(x+2)(x-5)`

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