Question

Find a polynomial equation for a function of zeroes of 0, -1 , 2.

A. f(x) = x(x-1)(x-2)
B. f(x) - (x+1)(x-2)
C. f(x) = (x-1)(x+2)
D. f(x) = x(x+1)(x-2)

Answer 1

A zero is going to occur wherever f(x) = 0. Which of those equations has 3 zeroes? Not B or C, because they only have a product of two terms. That leaves A and D. The naked x gives us a zero at x = 0. Still leaves both A and D. A zero at x = -1 means that we must have a product term = 0 with x = -1. Obviously, a term (x+1) = 0 if x = -1. Similarly, to have a zero at x = 2, we need a term (x - 2) = 0 if x = 2. So, to get zeros at 0, -1, 2 we need D, f(x) = x(x+1)(x-2).

Answer 2

Thank you so much! @whpalmer4

Answer 3

I think whpalmer4's got you covered with this "next" question of yours.