Which are real zeroes of this function? x³ + 2x² - 9x - 18

Solution:

To identify the zeroes of the function let the function:

f(x) =  x³ + 2x² - 9x - 18 = 0

Factorizing the polynomial we get:

f(x) = x²(x + 2) - 9(x + 2) = 0

f(x) = (x + 2)(x² - 9) = 0

We know that a² - b²  = (a + b)(a - b), hence x² - 9 = x² - 3² = (x + 3)(x -3)

f(x) = (x + 2)(x + 3)(x - 3) = 0

Hence the real zeroes of the function f(x) are 

x + 2 = 0 ⇒ x = -2

x + 3 = 0 ⇒ x = -3

x - 3  =  0 ⇒ x = 3

Hence the real zeroes of the function f(x) are x = -2, -3, and 3

Which are real zeroes of this function? x³ + 2x² - 9x - 18

Summary:

The real zeroes of the function f(x) = x³ + 2x² - 9x - 18 = 0 are x = -2, -3, and 3.