00:01
We have been told that we have an even degree polynomial.
00:05
That's the only thing we know about this polynomial.
00:08
And the statement that has been made, it must have at least one real zero.
00:19
Is that statement true? true or false? well, an even degree could be x squared, x to the fourth, x to the sixth.
00:28
Some even degree is my largest term.
00:30
Now, an even degree polynomial will look something like this.
00:35
I'm kind of putting some wiggles in the middle because i don't know exactly what the middle is going to do.
00:40
But the end results will either both go up or both go down.
00:44
And this is why.
00:45
Let me just do, for example, x to the 6th, a positive number will always give me a positive outcome in this kind of a case.
00:54
A negative number raised to an even exponent will also give me a positive outcome.
00:59
So whether x is positive or negative, both sides were going to go up.
01:06
Let's suppose i have a negative coefficient to this.
01:10
Well, that positive number for x of the 6 will become negative in both cases...