top of page
Finding the zeroes of an equation means finding the x-values for which the function, in this case f(x), is equal to 0.
​
Let us set the function's value to 0 and rewrite the equation.
0 = x³ + x² - 8x- 12
Finding the divisors for the constant
​
1, 2, 3, 4, 6, 12​
​
Brute Force
​
0 = 1 + 1 - 8 - 12 NOPE
​
0 = 8 + 4 - 16 - 12 NOPE
​
0 = 27 + 9 - 24 - 12 YEP
​
So we can factor out (x - 3)
0 = (1)³ + (1)² - 8(1) - 12
0 = (2)³ + (2)² - 8(2) - 12
0 = (3)³ + (3)² - 8(3) - 12
(x³ + x² - 8x- 12) / (x - 3)
Ruffini's method
x² + 4x + 4 = 0
(x + 2)(x + 2) = 0
(x + 2)(x + 2)(x - 3)
x + 2 = 0
x + 2 = 0
x - 3 = 0
zeroes
x = -2
x = 3
bottom of page