SOLUTION: Id have a question; I should find out what the possible rational roots of x^3 - 4x^2 + 2x + 1 are, I am not sure if 3.303, -0.303, 1 are right and I totally dont understand ho

Question 205169: Id have a question; I should find out what the possible rational roots of x^3 - 4x^2 + 2x + 1 are, I am not sure if 3.303, -0.303, 1 are right and
I totally dont understand how to use synthetic substitution, to find out which of the possible rational roots are actually a root of the equation. Could someone please help me with this?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
I should find out what the possible rational roots of x^3 - 4x^2 + 2x + 1 are, I am not sure if 3.303, -0.303, 1
----------------
It's easy to determine that 1 is a root. Then divide by x-1
--> x^2 - 3x - 1

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=13 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3.30277563773199, -0.302775637731995. Here's your graph:

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