00:01
We've been told that we have a fifth degree polynomial.
00:05
That's all we know about it.
00:07
Some fifth degree polynomial.
00:09
So it has somewhere in the polynomial, it has a term x to the fifth.
00:15
Maybe with a coefficient in front of it, maybe not.
00:18
And the question has been raised, or the statement has been stated, it cannot have exactly one real zero.
00:32
Is that statement true or false? well, let's think of what's happening.
00:37
If we have this fifth degree polynomial.
00:40
I'm going to just make the assumption that the coefficient is positive.
00:44
If the coefficient is negative, it will just mirror image.
00:48
It'll reflect the picture i'm drawing.
00:50
It won't affect the outcome at the end.
00:52
So i'm going to assume it has a positive coefficient.
00:56
If x becomes a larger and larger negative number, x to the fifth also becomes a larger and larger negative number.
01:03
A negative number time to an odd exponent.
01:08
Stays negative.
01:10
Now, as x becomes a larger and larger positive number, it will become positive...