Question

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

Answer 1

One possibility was f(x) = (x-1)(x-2)(x-3) is your polynomial. this will give you \[( x^{2} - 3{x} + 2) * (x-3) = x^{3} - 6x^{2} + 5x -6 \]. However this gives for x=0, the value -6, and you want -12, so we can tweak the original function to be f(x) = 2*(x-1)(x-2)(x-3). Note that this function does have zeros at 1, 2 and 3 as you want. (Substitute x=1, x=2, and x=3, and we get 0)

Answer 2

thank you