One root of f(x)=x3-9x2+26x-24 is x=2. what are all the roots of the function? use the remainder theorem.

All roots of the given function are, 2 , 3 and 4

Step-by-step explanation:

Given the function f(x) =

Also, it given that x=2 is a root of the function f(x).

So,  (x-2) is a factor of f(x).

Remainder theorem states that if a function is divided by (x-a), then the remainder is equal to f(a). If a function f(a) is equal to 0, therefore a is the root of the function.

We use synthetic method to divide f(x) by (x-2) as also shown in figure below;

To find the roots of the function f(x) equate f(x) = 0.

we have;

By zero product property states that if ab = 0, then either a = 0 or b = 0, or both a and b are 0.

x = 2 , 3 and 4.

Therefore, the roots of the given functions are; 2 , 3 and 4.

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction