SOLUTION: This is from a study guide for my final the question is: Find all the real and complex zeros of the polynomial x^4+4x^3-4x^2-36x-45 ...I know the answe involves 3, 2 and an ima

Question 41075: This is from a study guide for my final the question is:
Find all the real and complex zeros of the polynomial x^4+4x^3-4x^2-36x-45
...I know the answe involves 3, 2 and an imaginary number but I am having difficulty which ones are postive and negative etc...
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find all the real and complex zeros of the polynomial x^4+4x^3-4x^2-36x-45
The polynomial facors as (x-3)(x+3)(x^2+4x+5)
The zeroes are 3, -3 and the zeroes of x^2+4x+5 which are
worked out below:

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 -4 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 -4 is + or - .

The solution is

Here's your graph:

Hope this helps.
Cheers,
Stan H.
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