SOLUTION: Hi! hi A polynomial P is given. (a) Find all zeros of P, real and complex. 7x^3+7x^2+6x=0 (b) Factor P completely thanks for the homework help!

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Question 199844: Hi!
hi
A polynomial P is given.

(a) Find all zeros of P, real and complex.
7x^3+7x^2+6x=0
(b) Factor P completely
thanks for the homework help!
Found 2 solutions by Alan3354, cas199mss:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
(a) Find all zeros of P, real and complex.
7x^3+7x^2+6x=0
x = 0 is obvious. Factor out the x
7x^2+7x+6=0
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 : .

The discriminant -119 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 -119 is + or - .

The solution is , or
Here's your graph:

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(b) Factor P completely
Factoring out the x is all that can be done.
Answer by cas199mss(1)   (Show Source): You can put this solution on YOUR website!
yes
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