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 - 5x² + 2x + 8
Finding the divisors for the constant
​
1, 2, 4, 8
​
​
Brute Force
​
0 = 1 - 5 + 2 + 8 NOPE
​
0 = 8 - 20 + 4 + 8 YEP
​
So we found one factor now
​
(x - 2)
0 = (1)³ - 5(1)² + 2(1) + 8
0 = (2)³ - 5(2)² + 2(2) + 8
(x³ - 5x² + 2x + 8) / (x - 2)
Ruffini's method
x² - 3x - 4 = 0
(x + 1)(x - 4) = 0
(x + 1)(x - 4)(x - 2)
x + 1 = 0
x - 4 = 0
x - 2 = 0
ZEROES
x = -1
x = 4
x = 2
bottom of page