Question

The cubic function f(x) = z3 - 6x2 + 11x - 6 has a root at z = 3. a What are the other roots of the function?O r = 3, x = 2O r =-3, x = -2O x = -1, x = -2O x = 1, r = 2

Answer 1

Given the function f(x) as follows:

$f\mleft(x\mright)=x^3-6x^2+11x-6$

The function has a root at x = 3

We will use the synthetic division to find the other roots:

We will divide the coefficients by 3

As follows:

So, the given function will be written as follows:

$f(x)=(x-3)(x^2-3x+2)$

Factor the term of the quadratic function

$f(x)=(x-3)(x-2)(x-1)$

So, there are three zeros x = 1, 2, 3

So, the answer will be option 4) x = 1, x = 2