Question

One root of f (x) = x cubed minus 9 x squared 26 x minus 24 is x = 2. What are all the roots of the function? Use the Remainder Theorem.

Answer 1

The other roots of the function are 2, 3, and 4.

Given

One root of $\rm f(x)=x^3-9x^2+26x-24$  is x = 2.

What is the remainder theorem?

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

The one root of the function is;

$\rm x=2\\\\x-2=0$

Use synthetic method to divide f(x) by (x-2).

$\rm f(x) = (x-2) (x^2-7x+12)\\\\f(x) = (x-2) (x^2-4x-3x+12)\\\\f(x) = (x-2) (x(x-4) -3(x-4))\\\\f(x) = (x-2) (x-4) (x-3)$

Therefore,

All roots of the function are;

$\rm x-2=0,\ x=2\\\\x-3=0, \ x=3\\\\x-4=0, \ x=4$

Hence, the other roots of the function are 2, 3, and 4.

To know more about the Remainder theorem click the link given below.

https://brainly.com/question/3283462