Thread: Finding the remaining zeros of each polynomial function

Use the given zero to find the remaining zero's of each polynomial function.


P(x)= x^3+3x^2+x+3; -i



I'm pretty lost with this stuff. I've been watching Patrick's videos trying to remember my high school days but wow it's been a while hehe.

It looks like Conjugate Pair Theorem would be the way to solve. If I figure it out I'll post my solution.

If you guys could give me some direction to help me get back into the game that would be AWESOME!!

Thanks a TON

Originally Posted by RBlax

Use the given zero to find the remaining zero's of each polynomial function.


P(x)= x^3+3x^2+x+3; -i



I'm pretty lost with this stuff. I've been watching Patrick's videos trying to remember my high school days but wow it's been a while hehe.

If you guys could give me some direction to help me get back into the game that would be AWESOME!!

Thanks a TON

1. Since there are only real coefficients in the term of the function there must exist a 2nd solution x = +i. Thus must be a factor in the term:

2.

3. A product equals zero if one factor equals zero. Use this property to determine the last missing zero of P.

Hello, RBlax!

Use the given zero to find the remaining zeros.

. .

Since is a zero of , then is also a zero.
. . (Complex roots always appear in conjugate pairs.)

Then: . are factors of

. . That is: . is a factor of


Dividing, we find that: .


Therefore, the zeros of are: .


Edit: Too slow . . . again!
.

This isn't using the The Conjugate Pair Theorem though right?

I think what they are wanting me to do looks something like...



then use synthetic division (which I begin to become lost)

Edit: I'm slow too haha

But thanks a ton for the help.