Introduction
Content
Hello, how are you all right so uh to solve this equation? We need to understand some basic terminology, so let me just give you an example.
So if you have, if you have a quadratic equation like this one and they ask you to solve so there are some terminologies that you need to know.
First, you need to know product.
You need to know the sum you need to know factors.
So, once you get to know these three things solving quadratic equation, um will be simple for you of this nature and this one okay.
So now what is our product here? Our product will be a negative two.
So how did I know that it's a negative two I just got, or this is what you need to do.
You check whether it's part two and check the number that is in front.
So in this case you have a one and also check the number that has got no later a constant, so it will be 1 times negative 2, which is negative, two okay.
What about the Sun? What what is our son? In this case? Our son will be a one.
You just look at uh at uh, the point where we have X here, the number that is in front or the coefficient in this case there is the one he so this is the one.
Now what about the factors when we talk about factors, we are simply talking about two numbers such that when you multiply them, they give you negative two and when you add them, they give you a one okay.
So what are those numbers? It's actually negative one and a two of course.
So when we say negative one times, two, it's giving us a negative two uh negative one plus two, it's giving us a one.
Okay.
So once we reach this point, we reach this point.
We now arrange we, we we, we arrange our work so we're going to say X power 2 this x bar 2, where there is X here we substitute we are going to use the factors.
That's the reason why we decided to find the factors, so it would be.
Plus 2X, minus x, minus 2 is equal to 0., so I've just substituted.
If you're able to see what is here substituted these, so this one is the one which is right here and this one is the one which is right here.
We know that there is a negative one here, a one in front, so you just substitute them and then you are good to go.
Maybe your question may be: is there any order to follow in terms of putting these factors here? No, there is no order.
You can put them in whichever way you want to put them.
If you want, you can start with negative X, plus two, oh the weather.
So after doing this, you now factorize by grouping you see what I've done you check now.
What is it that is common? That is found here, and here it's X so write it outside.
Here we have X plus a 2.
You see.
This is what you remain with when you factor out X.
Here we remain with X.
Here you remain with two x and x.
Will cancel here will remain with only one X and then here, when you check what is it that is common? It's a negative one.
So here we remain with the X here like that, so this is what we have and you must make sure when solving a quadratic equation like this, that what is here and here are similar.
Can you see if they are different? Just know that what you're doing is wrong.
So after reaching this point, you now pick what is here x and what is here, minus c one write it inside.
You see.
We have these two, this one forget about it, pick the one which is here because they are similar.
So just pick one- and this is what we have you say equal to zero.
You see so now.
From this point you say: x, minus 1 is equal to zero or X.
Plus two is equal to zero.
Just get this equal to zero or this equal to zero.
Okay, next, you saw Bishop X is equal to a one.
This one will come this side.
It will be equal to the one here this one come this side.
It will be equal to negative 2.
So these are the two solutions for the example.
You have right here now.
Let's try to apply all these steps to this one okay and see how we do it will look like so I'm going to to leave this part this part, so that we can be making reference to this part right here.
So we have that 2 x, power, 2, plus 5 x, minus three is equal to zero.
So this is what we have: let's identify our product.
What is our product? It's negative six remember here to find the product we said one times negative.
Two, it's gave us a negative two.
The same applies here 2 times negative three, to give us a negative six, that's our product! Let's go to our sum, our sum we just pick the number that is here.
This is five.
Remember we go to the number which is here, which is a one here, it's a five.
What is our factors? We need to find two factors, so the factors will be two numbers such that when you multiply them, they give us negative negative six and when we add them, they give us a five.
So those two numbers are 6 and negative, one so six times negative one.
It's negative of six six plus uh negative one, it's a five, so we have the factors so upon identifying the factors we now substitute this.
So we have 2 x, power, 2, plus 6, x, minus x, minus 3 is equal to zero okay.
So you see I've just substituted them right here.
This is where they are here.
We get this and this substituted them there, and this is what we have so after doing this, you now factorize by grouping okay.
So here what is it that is common? It's a 2X, see 2x is found here and here because 2 can go into six and it can also go into two x can go into x, squared and x z.
So we shall X right here, plus here, it's a F3, this x and x will cancel 2 into 6 is a 3.
here, it's a negative one, which is common, which have X Plus F3, which is equal to a zero.
Remember what I said.
I said: what is here and here must be similar if they are different.
It means you've made a mistake somewhere, you need to check your work.
So next we shall, we shall say, 2x, minus 1.
Okay, remember we get this, and what is here.
This is what we put and also get this like that forget about this, which is equal to a zero okay.
Next we say, 2x minus 1 is equal to 0 or x.
Minus plus 3 is equal to zero okay, so here we solve for x, so we have 2X is equal to one.
You divide by two because we're solving for for x, divided by two this, and this will cancel.
We shall remain with x.
Uh will be equal to one over a two.
So this is our solution.
Okay, for this one, we just make this cross the equal sign.
It would be negative three, and this is our solution.
Thank you so much for watching I guess this video has helped you uh solving quadratic equations.
Please remember to follow me on my Facebook page and also to subscribe on my YouTube channel and also follow me on my Tick Tock, the same name that you're able to see Jacob, Percy chamber online, math, bye.
