00:01
So in this problem, we're being asked to use the intermediate value theorem to show that the given polynomial f of x has a real zero in between 1 and 2.
00:09
So the first thing we need to do is find f of 1.
00:13
To do this, we'll substitute 1 in place of x.
00:15
So we'll have 4 times 1 squared minus 2 times 1 minus 3.
00:20
Well, 1 squared is equal to 1, so 1 times 4 is 2 times 1 is 2, and now will subtract.
00:27
4 minus 2 is 2 and 2 minus 3 is 9.
00:30
Negative 1.
00:31
So that's our f of 1 value.
00:33
Next, we need to find f of 2.
00:35
So we'll substitute in 2 for x.
00:37
So we'll have 4 times 2 squared minus 2 times 2 minus 3.
00:42
We'll 2 squared is 4...