How do you find the polynomial function with roots 1, -2, and 5?

1 Answer
Alan P.
Jul 13, 2015

A polynomial function with roots 1, -2, and 5 would be
#f(x)=(x-1)(x+2)(x-5)#
Note however that there are infinitely many polynomial function with these roots.

Explanation:

If #k# is a root of a polynomial function #f(x)#
then #f(k) = 0#

Obviously, if #(x-a)# is a factor of #f(x)# then #f(a) = 0# and thus #a# is a root of #f(x)#.

Although there are infinitely many polynomials with the specified roots, all such polynomials in x will be multiples of f(x), i.e. they will have f(x) as a factor.

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