Hello in this quick movie I'm going to be introducing you to 'quadratic equations' and
the general form of the quadratic equation.
So first of all what is a quadratic equation? A quadratic equation in one variable is an
equation in which the greatest exponent of the variable is two, as in 6X square -6X-2=0
and Y squared -5Y+4=0.
This equation is in variable X and X is the only variable present here.
Similarly, this equation is in variable Y and Y is the only variable here.
You probably have already seen a pattern here: number times variable squared plus or minus
number times the same variable plus or minus number equal to zero.
Mathematicians call this pattern the general form, which is formally written as
aX square + bX + c = 0
If you compare the general form with the pattern
that we just came up with.
You should be able to see that they have used X in place of variable which is not necessary.
Y is also fine.
That is why I chose example 2 to be in variable Y. You will also find Z, W, P and Q
but X is used more frequently than the others.
Okay, now that these two are of the way.
Let's focus on A B and C. Again, if you compare it with this pattern you should see that A
B and C are in places of numbers. So X is a variable; A, B and C are numbers more precisely
real numbers.
But there is an exception.
A should not be equal to zero. we'll see why A cannot be equal to zero
In this very movie.
I know you have already understood this but just so that all of us are on the same page
let me make it clear. This means B equal to zero is fine. C equal to zero is also fine and even
if both of those are equal to zero
that is still fine.
By now you probably have a question.
In example 1
There are negative signs here, but the general form has only positives how come?
If you had this question, brilliant! But if you did not, I hope now you do.
And my answer is you will understand the reason as soon as we complete this simple exercise.
Let us focus on the first one for now it stays create a quadratic equation in variable X
with A=1, B=2 and C=3 so let's bring the general
form here. since the variable is supposed to be X.
These two are just fine.
A is supposed to be 1. So let's switch that out. B is supposed to be 2, and C is supposed
to be three and well that is the final answer No wait!
Mathematicians prefer to not write one as a coefficient. so let's drop that out.
Now let's move on to the next exercise which says create a quadratic equation in variable alpha
with A=5, B=0 and C= -25 If you do not know what alpha is
It is a Greek alphabet which is used as a variable in mathematics and other sciences.
You don't need to worry much about it.
Also here, B is equal to zero, but that is all right. Now, let's bring the general form. so the variable
is supposed to be alpha. Let's switch that. A is five and B is zero and C is -25
0 times alpha is 0, so that disappears. And we have five alpha squared -25 equal to zero.
We can simplify it further by dividing it by five. so we have alpha squared -5 equal to zero
Okay by now you probably have figured out the reason why there is no negative in the general form
but I'm gonna tell it to you.
Look at this equation, there is a negative here, but it came from C because C is -25
so if you think of it in a reverse manner, you should have the answer.
The gender form has only positive signs because negatives come from A, B and C.
okay now let's see why A should not be equal to zero, and between you and me
The best way to understand that is by equating it to zero, so let's reconsider this equation
and instead of A=1 we'll use A equal to zero.
Now zero times X squared is zero, so it disappears and we are left with 2X +3 equals zero and
this equation is not quadratic.
You probably can recognize this as a linear equation in one variable
so the conclusion
at A equal to zero.
Quadratic equations change to linear equations.
Therefore, we have this here. so that about wraps up this movie.
Check out the links in the description and please do the YouTube thing smash the thumbs up button.
If this was helpful or the thumbs down otherwise. share it with others and let me know your thoughts
or questions in the comments.
In the next movie we will discuss 'The zero product principal' and more.
And as always, thanks for watching