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

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Question 812135:
Find the roots of the polynomial equation: x^3 – 3x^2 + 9x – 7 = 0
Answer by tommyt3rd(5050) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B7+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A1%2A7=-24.

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 - sqrt%28+24%29+=+4.89897948556636.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B7+%29