Answer and Step-by-step explanation:
f(x) = x³ + x² - 4x - 4
Using the rational roots theorem we can determine that 2 is a root of this equation:
f(2) = 2³ + 2² - 4.2 - 4 = 8 + 4 - 8 - 4 = 0
By using Ruffini's rule we can find the others roots
2 | 1 1 -4 -4
1 3 2 0
x² + 3x + 2 = 0
S = -3 P = 2
x' = -1
x" = -2
roots are: -2 -1 2
sign before -2: f(-3) = -10 < 0
sign between -2 and -1: f(-1.5) = 0.875 > 0
sign between -1 and 2: f(0) = -4 < 0
sign after 2: f(3) = 20 > 0
This way, we can see the behaviour of the function