Precal Blog

Before break we talked about finding zeros for polynomials when we knew one of them for sure. (Either we were told what the zero was, or we produced a graph and found the zero by inspection.) After we knew one of the zeros, it is a simple matter of synthetically substituting the zero and then repeating the process with the resulting polynomial until we are down to a quadratic which we can factor by inspection or demolish with the quadratic formula.

Complex (non-real) zeros require a little more care when synthetically substituting but work the same way. You also need to remember that complex (non-real) zero’s come in conjugate pairs. So, if you have a zero 2 – 3i, then another zero must be 2 + 3i. Thinking about the way the quadratic formula works will give you some insight as to why this conjugate pair deal makes sense.

Someone should update the Wiki with the cubic polynomial sum of the zeros, pairwise products of the zeros, and products of the zeros stuff.

I haven’t really been feeling up to updating the blog recently, so my apologies to those of you that read it regularly. I will try to get back on a regular schedule soon.