Question

Please help, functions

Being f the function. with the domain IR (real numbers), defined by:

f (x) = x³ - 6x² + 11x - 6

Note: The answer should be 2 and 3 but I don't know how to get there, I need the resolution/explanation-

Answer 1

Explanation:

equate the equation to zero

x³-6x+11x-6=0

if we replace x with 1

it will result to zero

1³-6+11-6=0

using long Division

as shown in the picture

obtain

x²-5x+6

using factorisation

x²-5x+6

(x²-2x)-(3x+6)

x(x-2)-3(x-2)

x=2

x=3

x=1