How do you find the polynomial function with roots 2, #3+- sqrt2#?

1 Answer
sente
Dec 5, 2015

Start from the factored form to find the desired polynomial to be
#f(x)=x^3-8x^2+19x -14#

Explanation:

Creating a polynomial function with specific roots is as easy as can be. Just set it up as a product of binomials #(x-"root")# which evaluate to #0# at the desired root. For example, in this case, we would use

#f(x) = (x-2)(x-(3+sqrt(2)))(x-(3-sqrt(2)))#

#=x^3-8x^2+19x -14#

Because we start from the fully factored form, it is clear that the roots are as desired.

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