WEBVTT 00:00.220 --> 00:03.910 This is the last lecture of this section. 00:03.960 --> 00:07.130 So that means we should be doing some practice problems. 00:07.470 --> 00:11.070 So let's start with problem one. 00:11.110 --> 00:13.540 What does result evaluate to us. 00:13.570 --> 00:22.290 We have some int x is called the Zero and Y is equal to 20. 00:22.320 --> 00:30.330 We have a boules head which is equal to true and W which is equal to false. 00:30.390 --> 00:34.570 So what would results evaluate. 00:35.160 --> 00:38.230 So we have w so w. 00:38.370 --> 00:41.960 So not false is true or true. 00:42.030 --> 00:45.960 So this whole thing is true here. 00:47.990 --> 00:57.110 True or true is true and we're ending this with STR in inside these parentheses. 00:57.360 --> 01:07.340 So why is greater than x y is 20 so 20 is definitely greater than zero. 01:08.030 --> 01:12.480 And Zed is true. 01:12.480 --> 01:19.150 So not Zed is false so true and false is false. 01:19.880 --> 01:21.160 But then we negate it. 01:21.170 --> 01:25.730 So true and true is true. 01:25.730 --> 01:33.440 So if you run this should see this is true. 01:33.540 --> 01:36.690 So Gallia result is 1. 01:36.770 --> 01:40.180 So it's true. 01:40.200 --> 01:43.400 So let's move on to the next problem. 01:43.400 --> 01:48.440 So write a program that finds all the roots of the quadratic equation. 01:48.440 --> 01:55.550 So a quadratic equation is in the form of X squared plus B X C equals zero. 01:56.000 --> 02:09.930 And we'll remember at how you get the roots are B minus or negative be sorry plus square root of B squared 02:10.830 --> 02:22.840 minus 4 A C all over today and negative b minus a square root of B squared. 02:23.790 --> 02:28.380 Minus 4 A C over all over 2. 02:28.770 --> 02:42.060 So let's try to unpack this a little bit so we know that the quadratic equation can have either 1 or 02:42.060 --> 02:50.070 2 real or complex roots depending on the discriminant and the discriminant. 02:50.070 --> 02:51.860 Is this Partch. 02:52.350 --> 02:56.630 It's whatever's under underneath the square root side. 02:56.660 --> 03:03.800 So say this was negative then this would be an imaginary number. 03:04.750 --> 03:13.690 So this whole thing would be imaginary but if it's positive then this is a real number. 03:14.400 --> 03:23.470 And if this is ZERO say these are exactly the same then this whole thing would be zero. 03:23.490 --> 03:27.810 So we kind of have three different cases. 03:27.840 --> 03:29.040 Case one 03:31.660 --> 03:33.410 is discriminant. 03:36.870 --> 03:47.690 Is positive meaning it's a real real Rich case to 03:50.670 --> 03:55.710 is the discriminants is zero. 03:57.510 --> 04:07.820 In case three is the in CH is 04:12.930 --> 04:23.890 so we know now that we two have some kind of if statement and that condition will be whether the discriminant 04:23.890 --> 04:27.080 is positive negative or zero. 04:27.370 --> 04:39.420 So we will need a in this statement it's just the way. 04:39.820 --> 04:43.410 So how will this work. 04:45.450 --> 04:48.340 Well or you need some very well Seer's. 04:48.410 --> 04:49.590 It's a 04:51.970 --> 04:56.110 in the C. 04:56.380 --> 05:07.130 So this will match with the A here B here and see here and we're going to need some floats for the roots. 05:07.560 --> 05:10.530 One two 05:15.370 --> 05:16.000 one 05:19.120 --> 05:19.790 you 05:22.100 --> 05:27.480 in say the imaginary right now 05:31.910 --> 05:37.390 and we also need the discriminant is while 05:44.240 --> 05:50.300 we know what the discriminant should be say it's imminent. 05:51.670 --> 06:01.630 Sequel to the times b actually before I'll just finish this line four times. 06:04.630 --> 06:20.500 A C before this we need to actually get a B and C S A C out integer values A E 06:23.480 --> 06:26.170 and C. 06:26.540 --> 06:29.250 The dreaded 06:32.540 --> 06:33.700 equation. 06:37.030 --> 06:49.220 A X power to us e times x plus c 0. 06:49.250 --> 07:02.550 So we need to see in three different E's here now throw floats because Ewing's division. 07:02.790 --> 07:06.750 So we get a B and C we determine the discriminant. 07:06.750 --> 07:11.170 Now we have to check to see if the discriminant 07:15.040 --> 07:16.320 is greater than zero. 07:16.330 --> 07:23.550 That means positive positive case right. 07:24.360 --> 07:28.820 So we have we know how to do this one. 07:28.980 --> 07:32.130 It's Roueche of negative B 07:35.920 --> 07:37.100 plus. 07:37.430 --> 07:40.780 But we don't know how to square root something. 07:40.950 --> 07:43.700 So this is kind of a problem. 07:43.860 --> 07:53.790 So in fact we can actually do our very first extra include and often include something called C math 07:54.920 --> 08:04.980 in C math has a bunch of math functions that we can use in those math functions is called s u r th square 08:04.980 --> 08:05.770 root. 08:06.150 --> 08:11.490 So we need the square root function to see her him and then each 08:15.920 --> 08:18.730 hardware spill over 08:24.050 --> 08:27.020 all over 2 times a. 08:27.280 --> 08:35.750 This is just us following the formula that was outlined right here minus B plus square root the discriminant 08:35.760 --> 08:41.790 which is the squared minus for a C over to. 08:42.150 --> 08:44.590 Hey that's the very first one. 08:47.400 --> 08:49.440 In ch 08:54.060 --> 08:54.580 to 08:57.390 --> 09:01.710 minus B minus where. 09:03.590 --> 09:05.020 Is permanent. 09:05.100 --> 09:08.270 Which over 09:20.130 --> 09:21.660 Interesse C out. 09:23.810 --> 09:28.030 To sting. 09:29.700 --> 09:33.310 Real roots this 09:39.160 --> 09:42.220 one and 09:46.790 --> 09:47.000 two 09:53.500 --> 09:59.860 okay in either case is house if it is permanent. 10:02.270 --> 10:05.330 Is less than zero. 10:05.750 --> 10:07.600 So it's negative here. 10:09.070 --> 10:12.800 Which means you have some imaginary number. 10:12.850 --> 10:13.350 Right. 10:13.490 --> 10:16.690 So a square root some negative value. 10:16.690 --> 10:18.360 You get an imaginary number. 10:18.370 --> 10:33.590 So Roueche one equals two minus the over two times a. 10:33.770 --> 10:35.230 It's just part of the root 10:38.760 --> 10:40.670 Ch 1. 10:40.790 --> 10:45.710 So they're both the same now and then this imaginary parch 10:48.720 --> 10:50.400 called square root. 10:55.300 --> 11:04.300 The positive version of the discriminant right a meta make negative mean discriminant is already negative 11:04.310 --> 11:10.130 so we make that positive by by putting this minus sign in front of it. 11:13.750 --> 11:18.720 So square the discriminant over two times. 11:20.540 --> 11:25.360 Again we're just are really just following the formula. 11:25.380 --> 11:26.810 No real difference. 11:28.070 --> 11:29.780 And then we say C ouch 11:33.010 --> 11:36.600 to this thing. 11:40.670 --> 11:42.330 Complex roots 11:46.410 --> 11:47.090 just 11:53.020 --> 11:54.190 she is 11:57.810 --> 11:58.340 one 12:01.140 --> 12:03.010 and then last I 12:05.690 --> 12:06.770 imaginary 12:09.710 --> 12:12.110 number and 12:16.540 --> 12:17.160 two 12:23.210 --> 12:24.020 minus 12:26.530 --> 12:29.860 the imaginary number. 12:37.170 --> 12:41.380 So again we're just really just following the formula that was outlined here. 12:43.360 --> 12:47.160 And we're just doing decisions based on the discriminant. 12:47.580 --> 12:49.470 Otherwise it has to be zero. 12:49.500 --> 12:50.050 Right. 12:50.920 --> 12:54.670 So Roueche 1 equals 12:58.620 --> 13:07.090 Nate e over to a a. 13:07.280 --> 13:08.660 And that's it. 13:08.900 --> 13:19.880 Because if this is zero this whole part is zero Roueche two equals one they're the same 13:22.440 --> 13:27.410 so see Ouch two equal 13:29.750 --> 13:30.510 Greil 13:32.670 --> 13:35.020 reduce exists. 13:39.810 --> 13:40.410 One 13:43.610 --> 13:44.030 and 13:47.320 --> 13:47.530 Two 13:51.930 --> 13:52.950 you run this 14:00.440 --> 14:05.840 it's bigger so you just give it some random values. 14:06.740 --> 14:09.210 1 0. 14:09.460 --> 14:16.330 So those are two real roots and it's zero point five 14:18.720 --> 14:26.040 see could we make this zero. 14:26.260 --> 14:27.160 B was 14:29.810 --> 14:30.500 you 14:35.200 --> 14:50.840 two two and one Verio two distinct complex roots negative two plus imaginary I 0.5 in needed two is. 14:51.100 --> 14:56.490 I see your point but so this should be working. 14:56.510 --> 14:59.760 Think so. 14:59.760 --> 15:02.260 Move on to the next one. 15:09.680 --> 15:20.170 Each program that enters and number and prints out whether it's even or not use a switch. 15:20.320 --> 15:26.540 Get rid of this. 15:32.550 --> 15:39.360 So we need a number of cells just say number zero say. 15:41.400 --> 15:44.850 Enter any number. 15:45.170 --> 15:45.540 Sure 15:48.740 --> 15:52.250 if it's even more odd 15:58.040 --> 15:59.250 that get that number 16:07.500 --> 16:10.770 and then we'll see two results here. 16:12.080 --> 16:16.930 Equals to number modulus 2. 16:17.510 --> 16:22.780 So remember what modulus was it gets the remainder of the division. 16:22.790 --> 16:30.650 So whatever the number is it'll be divided by two and then the remainder will get set to result. 16:30.650 --> 16:34.290 So the remainder can only be two values here. 16:34.520 --> 16:39.030 So it could either be 0 or 1. 16:39.390 --> 16:42.240 So if you say switch on the results 16:45.830 --> 16:56.060 and then you have case 0 this means it would be even right evenly divides there's no remainder number 16:56.260 --> 16:57.610 is even 17:01.150 --> 17:06.090 in break and you need those breaks. 17:06.090 --> 17:08.870 Case 1 is out. 17:10.520 --> 17:16.190 Number is odd because it had a remainder. 17:16.190 --> 17:23.910 There is a one remaining brick on this. 17:24.340 --> 17:33.120 So 31 numbers on it's right in say 20. 17:33.160 --> 17:43.000 So the numbers even so memory that modulus gets the remainder of the division between the two numbers. 17:43.490 --> 17:45.320 And this is an integral type. 17:45.320 --> 17:46.580 It's just an integer. 17:46.760 --> 17:52.270 So you can switch on it and you have cases which is consonant expressions. 17:52.420 --> 17:58.720 So 0 and 1 are constant expressions and all match which one fits best. 17:58.970 --> 18:04.030 And we break because we don't want to fall through and do the cases below. 18:04.400 --> 18:08.040 And notice we don't have a default here because we don't really need it. 18:09.200 --> 18:10.100 So that's it. 18:10.100 --> 18:16.880 I hope you do the practice problems in the next lecture and I'll see you in the next section.