Question

What is the third–degree polynomial function such that f(0) = –12 and whose zeros are 1, 2, and 3?

Answer 1

use the fact that an n'th degree polynomial with roots \(x=r_1,x=r_2,...,x=r_n\) can be written as:\[f(x)=C(x-r_1)(x-r_2)...(x-r_n)\]where C is some constant.

Answer 2

example: if a second degree polynomial has roots 4 and 5, and has f(0)=40, then we can write it as:\[f(x)=C(x-4)(x-5)\]then make use of the fact that f(0)=40 to get:\[40=C(0-4)(0-5)=20C\implies C=2\]therefore:\[f(x)=2(x-4)(x-5)\]