SOLUTION: solve:X^3-4X^2+4X+48=0

Question 624418: solve:X^3-4X^2+4X+48=0
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
To solve an equation like this one would normally factor it. But if the expression you posted does not factor:

The greatest common factor of is 1 (which we rarely bother factoring out).
has too many terms for any of the factoring patterns.
has too many terms for trinomial factoring
I can see no way to factor it by grouping.
The possible rational roots of are:
1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 8, -8, 12, -12, 16, -16, 24, -24, 48 and -48
But none of these are roots.

If there was an error in what you posted then re-post your problem. If there were no errors, then keep reading...

Below are two graphs of gives you a high-level view showing the "interesting" parts of the graph and the second one uses a differnt scale on the x-axis. This gives us a horizontally stretched view so we can better see some of the features of the graph, especially the x-intercept). (The x-intercept(s) would be the solution to your equation because x-intercepts have y values that are zero.)

As you can see from this high-level view, the graph crosses the x-axis just once. This means that there is only one real solution to your equation. (Note: The graph does not "bend around" and come back to cross the x-axis outside of what we see here.)

As you can see from this stretched view, the graph crosses the x-axis somewhere between -2 and -3. None of the possible rational roots were between -2 and -3. This tells us that the one real solution is an irrational number between -2 and -3.

There is a formula for cubic equations but it is very complex and not often taught in Math classes. Click here if you want to see it.

If you have a graphing calculator and know how to use its trace function. you could find a decimal approximation for the solution to your equation. Just trace to the x-intercept.
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