Persamaan Kuadrat [Part 1] - Bentuk Umum Persamaan Kuadrat

Hello everyone, meet again with Mr. Benny. I hope you are there in good health. In the previous video, Mr. Benny has discussed the first chapter, namely the division and the root form. In this video, Mr. Benny will discuss the next chapter, namely the equation and the function of the first quadrant, about the general form of the equation. So, prepare your writing tools, let's start.

Okay, first Mr. Benny will explain first the purpose of watching this video.

After watching this video, you are expected to be able to understand the meaning of the square and the general form, then differentiate which is the square and which is not the square. Okay, let's just start with the first one, understanding the meaning of the square and the general form. Okay, what is a square? A square is a combination whose variable has the highest level of 2.

The general form is like what Mr. Benny gave the yellow box, ax^2 + bx + c = 0. The condition is that a cannot be 0. Why can't a be 0? Because if a is 0, it means 0 * x^2 + bx + c = 0. 0 * x^2 = 0, so this is over.

then the equation becomes bx + c. Well, bx here, if it's not written, it means that x is the first grade. Well, even though the square equation has to be two, here the first grade is only one. That's why the a can't be zero. If it's zero, it means it's not a square equation. You can understand, right?

Now here Mr. Benny press again that A is the number in front of X squared, B is the number in front of X only, while C is the number without the variable. Or another name later if the number without the variable is called Constanta. Okay? So the number without the variable or no letter, only numbers, is called Constanta.

We must be consistent with this, so A is in front of X squared, B is in front of X, C is without the letter. Why? Because later there will be a formula that is related to this. So keep consistent.

Okay, let's just continue to the example so that you can understand better. Okay, continue. Here is the example. Among the following equations, which one is the square equation? Let's just check the first one. x squared + 4x - 21 = 0. Is this a square equation?

Let's check the highest level. Here is x^2, so it must be a square. Now let's check the ABC. A means the number in front of x^2. In front of x^2 there is no number. Remember, if there is no number, it means 1. And people usually don't write the number 1. But if it's not written, it means 1. Okay, you can understand, right? So, A = 1.

B is the one in front of X, which means 4, right? So B = 4. Continue again, C =? C is the number without the variable. The variable is X, so we just look for the number that doesn't use X. It means 21. But be careful, in front of it there is a minus, right? So C is -21, like that. Can be understood, right?

Next, 24y-8y^2=0. This is using y, not using x. It's okay. So the variable doesn't have to be x. So it doesn't have to be x, it can be y, a, b, c, whatever the question is.

Now the variable is Y. We check the highest level. Here the highest level is 2. This means this is a square equation. We check the ABC. A in front of Y squared. The one in front of Y squared means -8. So here A is

-8 Okay continue B B in front of Y in front of Y is 24 means B = 24 continue again C = C which does not have a variable here there are all variables so C is not there, right? Yes, C = 0 like that, okay, it's easy, right?

Continue again, is this a square equation? The bottom left first, 2x ^ 3 - x ^ 2 + 5x - 4 = 0. Here, there is indeed a 2nd place, but the requirement for a square equation is the highest point, it must be 2. It turns out that the highest point here is the 3rd place. So this is not a square equation. Okay, it can be understood, right?

Continue again, next is k^2 = 9, is this a square equation? Well, to make sure, we change to the general form first, right? The general form must be equal to 0, so this will be k^2, 9 move to the left, so -9, right? So -9 = 0. Now, is this a square equation?

Of course, the square is the same, because the highest level is the second level, right? Okay, so here it is correct, the square is the same. Let's check the ABC. A, which is in front of the second level. In front of K, the second level means there is no number, right? It means it's the same as 1. Continue, B. B is the one in front of K, it should be. But K is not there, right? It means B is 0. Continue, C.

C is just a number, which means -9. Okay, you can understand, right? About determining whether it is a square or not. And also determine the value of ABC. Okay, easy, right? Okay, continue again, so that you understand more, Mr. Benny gives another example. Change the following equation into the general equation of the square. Remember, the general equation of the square is like what Mr. Benny gave the yellow box.

So, ax^2 + bx + c = 0. So it must be equal to 0. If it's not equal to 0, we change it. Why? Because the general form is equal to 0. Okay. Here, because x^2 = 3x - 1. We have to move this 3x - 1 to the left. So that it is equal to 0. Okay, so 3x - 1 move it to the left.

Okay, continue. So the one on the left is x squared. 3x, move to the left, so it's minus 3x. Minus 1, move to plus. Min, move to plus. So this is plus 1 equals 0. Now this is the general form of the square equation.

Next, if asked for ABC, we check the A. A is in front of X^2. If there is no number, it means 1. So A = 1.

The one in front of X is B. The one in front of X is -3. So here B is -3. Continue again, C is the number. So it's 1. So C is equal to 1. Easy, right?

Okay, let's continue to the last example in this video. Change the following equation to the general form of the square equation. Here it may look complicated, but actually it's not as difficult as you imagine. Just be patient, let's work. The point is, the right side must be equal to zero, right? Okay, let's start. 2 times x squared, which means 2x squared.

2 times 5 means this is 10, right? Equals x times x, x squared, x times minus 7 equals minus 7x. Okay now, this one, the right one, x squared minus 7x, we want to make it zero, so everything has to be moved to the left. You can understand, right?

Continue, which means that the one on the left will be 2x squared plus 10. Well, x squared, move to the left, so minus x squared. Minus 7x, move to the left, so plus 7x. The point is the opposite, if it is positive, it changes to negative. If it is negative, it changes to positive. It means that the one on the right is finished, it has changed everything, it means it is equal to 0.

Continue, 2x^2 we can simplify it with x^2 too, so 2x^2 - x^2 = x^2 Then we arrange, now the one with x, it means that there are only 7x, then add 7x

then the one without X means there are only 10 right? means +10 = 0, this is the general form x squared + 7x + 10 = 0 if asked for ABC, let's see, A is in front of x squared, means 1, B is in front of x, 7

So C doesn't use X, so it's 10. Okay, easy right? Okay, that's the video for the general formula of the square. For the next video, Mr. Benny will discuss how to determine the square root of the equation using the method of factorization. So stay tuned. I hope this video is useful. Thank you for watching. And ciao!

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