Find a cubic function with the given zeros. 6, -3, 5

Solution:

Since the given zeros of the functions are 6, - 3, 5 we can write

x = 6 ⇒ x - 6 = 0 --- (1)

x = -3 ⇒ x + 3 = 0 --- (2)

x = 5 ⇒ x - 5 = 0 --- (3)

The three factors which of the cubic function are (1), (2) and (3) and we can write:

(x - 6)(x + 3)(x - 5) = 0

(x² - 3x - 18)(x - 5) = 0

(x³ - 5x² - 3x² + 15x - 18x + 90) = 0

x³ - 8x² - 3x + 90 = 0

Hence the cubic function whose three roots are 6, -3, and 5 is x³ - 8x² - 3x + 90 = 0

Find a cubic function with the given zeros. 6, -3, 5

Summary:

The cubic function with the given zeros. 6, -3, 5 is f(x) = x³ - 8x² - 3x + 90 = 0