SOLUTION: Find the roots of the polynomial equation: x^3 � 3x^2 + 9x � 7 = 0

Question 812135:
Find the roots of the polynomial equation: x^3 � 3x^2 + 9x � 7 = 0
Answer by tommyt3rd(5050) (Show Source): You can put this solution on YOUR website!
x^3�3x^2+9x�7=
x(x^2-2x+1)-(x^2-8x+7)=
x(x-1)^2-(x-1)(x-7)=
(x-1)[x(x-1)-(x-7)]=
(x-1)(x^2-x-x+7)=
(x-1)(x^2-2x+7)
the last two are irrational so...

Solved by pluggable solver: SOLVE quadratic equation with variable

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 : .

The discriminant -24 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -24 is + or - .

The solution is

Here's your graph:

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