Question

One root of f(x)=x^3-9x^2+26x-24 is x = 2. What are all the roots of the function? Use the remainder theorem

Answer 1

x = 2, x = 3, or x = 4

Explanation:

A on edg 2022

Answer 2

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

Explanation:

The given function is

`f(x)=x^3-9x^2+26x-24`

It is given that x=2 is a root of the function. So (x-2) is a factor of f(x).

According to 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.

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

`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)`

To find the roots equation the function equate the function equal to 0.

`0=(x-2)(x-4)(x-3)`

Equate each factor equal to 0.

`x=2,3,4`

Therefore the roots of the function are 2,3 and 4.