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

1 Answer
sente
Dec 19, 2015

Begin with the factored form to find that one such polynomial is

#P(x) = x^3 +2x^2 - 13x + 10#

Explanation:

A simple way of generating a polynomial with given roots is to begin with it in factored form. If #(x-x_0)# is a factor of a polynomial #P(x)#, then #P(x_0) = 0# and so #x_0# is a root of #P(x)#.

Applying this here, we get

#P(x) = (x-(-5))(x-1)(x-2)#

Again, plugging in any of the desired roots immediately yields #0#, meaning the polynomial has the desired properties. Then, all that remains is to multiply it out.

#P(x) = (x+5)(x-1)(x-2)#

#= x^3 + 2x^2 -13x + 10#

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