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. X = 2, x = 3, or x = 4 x = –2, x = –3, or x = –4 x = 1, x = 2, x = 3, or x = 13 x = –1, x = –2, x = –3, or x = –13.

Answer 1

The roots of the given function is $\rm F(x)= x^{3}-9x^{2} +26x-24$ are 2,3&4

Given: x=2 is a root of the function. So, (x-2) will be a factor of this function

What is Remainder Theorem?

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

Here we will use the synthetic division method to divide the function f(x) by (x-2).

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

In order to find the roots of the given equation the function we equate the function equal to 0

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

Learn more about Linear Equations here : https://brainly.com/question/26387159

Answer 2

Answer:  A: x = 2, x = 3, or x = 4

Step-by-step explanation: EDG 2022