SOLUTION: I need help to figure out a math problem: 3x to the 3 power

SOLUTION: I need help to figure out a math problem: 3x to the 3 power - 9x to the 2 power+12x

Question 250255: I need help to figure out a math problem: 3x to the 3 power - 9x to the 2 power+12x
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
equation is:

3x^3 - 9x^2 + 12x

this looks like a quadratic equation in disguise.

factor out an x to get:

x * (3x^2 - 9x + 12)

set the equation equal to 0 and solve for the roots.

x * (3x^2 - 9x + 12) = 0

factor out a 3 to get:

3 * x * (x^2 - 3x + 4) = 0

x^2 - 3x + 4 cannot be factored because the roots are not real.

here's a graph of x^2 - 3x + 4

you can see that it doesn't cross the x-axis so it's roots are not real.

each one of the factors can be set equal to 0.

3*x = 0 yields x = 0

you have a solution at x = 0.

your equation of:

3x^3 - 9x^2 + 12x = 0 becomes 0 when x = 0.

If you make the equation equal to:

y = 3x^3 - 9x^2 + 12x, then you will have a value for y whenever x is a real number which it will always be because there are no restrictions on the domain of this equaion.

a graph of this equation looks like this:

I can't think of anything else to do with this equation.

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