The cubic function with the roots is f(x) = x³ - 6x² - 19x + 84
How to find the function
The function is sought b finding the equation in factored form and expanding
The equation in factored form
x = 3, (x - 3)
x = -4, (x + 4)
x = 7, (x - 7)
f(x) = (x - 3) (x + 4) (x - 7)
Expanding the equation
f(x) = (x - 3) (x + 4) (x - 7)
f(x) = (x² - 3x + 4x - 12) (x - 7)
f(x) = (x² + x - 12) (x - 7)
f(x) = x³ - 7x² + x² - 7x - 12x + 84
f(x) = x³ - 6x² - 19x + 84