00:02
So in this problem, we're given f of x equals a negative 0 .5x squared plus 2 .5x plus 4 .5.
00:20
And asked to determine several things.
00:24
First of all, we're asked to determine the real roots and graph this function, of course, and use the bisection method to determine the highest route with an employed guess.
00:40
It's the initial guess of five and the upper guess of 10.
00:50
Okay.
00:50
And to do the estimated error, estimated error, and the true error.
01:09
So first of all, let's graph this function just for a second here.
01:13
So i got y, not capital y, a little y, equals.
01:19
Negative 0 .5 x squared plus 2 .5 plus 4 .5.
01:45
And so what do we see? we see two roots here, don't we? see that one at negative 1 .405.
01:54
So x1 is negative 1 .405 and x2.
02:01
The other root over here at 6 .405.
02:07
0 .405.
02:09
Okay.
02:11
So that gives us the two roots.
02:19
We did it by the quadratic formula.
02:21
We'd have x equals minus b plus or minus a square root, b squared minus 4a, all over 2a.
02:32
Well, let's see.
02:35
We're wondering to this when the f of x is zero.
02:38
So zero equals.
02:40
And we noticed that we can multiply by 10 and clear out all the decimals.
02:46
And if we multiply by negative, that gives us a positive coefficient at the beginning.
02:51
So we now have 5x squared minus 25x minus 45, wouldn't me? okay.
03:02
And so then that means this is a, this is b here, and all this is c.
03:10
Okay.
03:12
So that would mean that x now is minus b, that's 25, plus or minus a square root of b squared, that's minus 25 squared, minus 4 times a, which is 5, times c, which is a minus 45, all over 2a, which is 2 times 5.
03:45
So when you do these out, multiply all this out and work through the two solutions, you're going to get x equals minus 1 .405, and x is a positive 6 .405...