Problema Solution
2. Heinz has a list of possible functions. Pick one of the g(x) functions below, show how to find the zeros, and then describe to Heinz the other key features of g(x).
• g(x) = x3 – x2 – 4x + 4
• g(x) = x3 + 2x2 – 9x – 18
• g(x) = x3 – 3x2 – 4x + 12
• g(x) = x3 + 2x2 – 25x – 50
• g(x) = 2x3 + 14x2 – 2x – 14
Answer provided by our tutors
g(x) = x^3 – x^2 – 4x + 4
click here to see the graph of the function
from the graph we see the function has 3 zeros (there are 3-intersection with the x-axis)
x^3 – x^2 – 4x + 4 = x^2(x - 1) - 4(x - 1) = (x - 1)(x^2 - 4) = (x - 1)(x - 2)(x + 2)
thus the zeros are
x1 = 1
x2 = 2
x3 = -2