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!

Algebra ->  Polynomials-and-rational-expressions -> 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!      Log On


   

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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 7x%5E2%2B7x%2B6+=+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=%287%29%5E2-4%2A7%2A6=-119.

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 - sqrt%28+119%29+=+10.9087121146357.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+7%2Ax%5E2%2B7%2Ax%2B6+%29

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(b) Factor P completely
Factoring out the x is all that can be done.

Answer by cas199mss(1) About Me  (Show Source):