Question

Find all real zeros of the polynomial function. f(x) = 6x^3 − 24x^2 + 12x ?

Answer 1

0, 1, 3

Explanation:

To solve this, we set the equation equal to 0 and factor it. First, we can factor out 6x to get `6x(x^2-4x+3)=0`.

Next we can factor out the area in parentheses. To do this, we need to find two numbers that add to -4 and multiply to 3. Those two numbers are -1 and -3. This means that we can write the equation as:

`6x(x-1)(x-3)=0`

For the expression to be equal to zero, at least one of the multiples must be also equal to zero. This means that we can solve by setting each multiple equal to zero.

`6x=0 => x=0`

Or:

`x-1=0 => x=1`

Or:

`x-3=0 => x=3`