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#### 如何简单破解一元二次方程式

How to Factor any Quadratic Equation Easily - Trick for factorising

G’day, welcome to Tacmath Channel.

What we’re gonna be having a look at today’s video

is how to factorize quadratic equations really simply, really easily.

So I’ll put an example up for you.

So the equation we’re going to have a look at is this one,
2x²+7x-4=0
2x squared plus 7x take away 4 is equal to 0.

Now, how do we tackle this one? Really simply.

We are just gonna look at the coefficients, that is the numbers in front of our x squared or x here,

as well as this our constant here, there’s negative 4, to get our answer.

So we’re just gonna label this.
A是2 B是7
We got A which is a 2, we got B which is a 7
C是-4
and C which is a negative 4.

It’s gonna be the same pattern again and again, whatever you solve any of these.

Ok, so the first thing we do after we do that is

we just go A times C, this first number times the last number.

2 times negative 4,

2 times negative 4 is equal to negative 8.

We’re just gonna use this middle coefficient here for our next part which is B.
B在这里是7
B is equal to 7.

Now what? Well, we’re gonna look for two numbers – two factors of negative 8.

Then when you multiply, you have negative 8,

they would make the factors of negative 8,

but when you add them, give us 7.

So two numbers you multiply to give negative 8 but add to give 7 here.

The factors of negative 8 that add to give 7 are the following

we have 8 and negative 1.

Ok, because when we multiply 8 times negative 1, we get negative 8.

But when we get 8 and negative 1 and put them together,

we get 8 minus 1 which is 7.

Now what? Well, pretty simple.

We are just going to change the signs on these.

What I mean by that is

all things negative will become positive and all things positive will become negative.

Negative 8 and positive 1, just flip those around.

Last of all, we’re just gonna put this over, the coefficient A here, ok, the very first one here,

divided by 2, divided by 2.

And this gives us here two values for x.

What x could equal? X could be equal to negative 8 over 2,

so negative 8 divided by 2 is negative 4

or x could be also equal to positive 1 over 2 which is a half.

Pretty simple, right? Just remember that pattern, ok?

Let’s have a look at another one.

The next one we’ll have is
2x²-2x-12=0
2x squared minus 2x minus 12 is equal to 0.

You give it a fly.

Ok, we have A B C.

We’re gonna multiply A times C,

this is equal to 2 times minus 12, which is minus 24.
B是-2
B is equal to negative 2.

What numbers multiply to give negative 24,

but then you can put together to get negative 2?

4 and minus 6.

Again, because if you multiply 4 and minus 6, you get negative 24,
4减去6等于-2
but if you go 4 take away 6 you get negative 2.

So what do we do?

We are going to flip the symbols here,

everything negative becomes positive, everything positive becomes negative.

We have negative 4 and positive 6

and we are going to put these over, you got it? this coefficient here, over 2.

And these are gonna be our two solutions.

X is going to be equal to, to solve this,
-4除以2等于-2
minus 4 divided by 2 which is negative 2,

or 6 divided by 2, which is 3.

Ok, how’d you go with that? Let’s make it even harder.
-10X²+13X+3=0
All right, minus 10x squared plus 13x, plus 3 is equal to 0.

Give this one a go. I’ll give you a little heads up.

There’s a bit of a trick with this one, ok?

Just be careful of your factors.

All right, so A B C. Hit pause if you’re good at it, ok? Let’s just go

A times C which is equal to, now minus 10 times 3, which is negative 30.
B是13
And B is equal to 13.

Now, well I can see there’s a bit of trick with factors here.

Do you wanna look at it and think it okay with 10 and 3 ?

because you know 10 and 3 can be used to get 13.

But they don’t do their factors, ok?Because, it’s gonna go to a negative.

It’ll has to be 10, negative 3 or negative 10 and 3.

You can’t put those together to get 13.

In fact, their factors are the following and factors are going to be
15和-2
15 and negative 2.

Because we multiply these to get 30
15减去2等于13
and we put 15 take away 2 is 13.

So they’re the two factors.

Once again, black becomes white and white becomes black,

negative becomes positive, day becomes night.

And negative 15, positive 2.

And we put those over the coefficient.

To be honestly, what x is equal to,

the coefficient is negative 10, negative 10.

Ok, so negative 15 divided by negative 10,

x could be equal to,

ok, that’s gonna cancel each other out,
15除以10等于1.5
15 divided by 10 is one and a half.

2 divided by minus 10, we got a negative one-fifth.

How did you go with that?

I’ll tell you what, we’ll get a doozy for the last one.

Here we go, 6x squared take away x, take away 2 is equal to zero.

Solve for X a

Now this is gonna be as easy as, you know where I’m going with this, A B C.

A times C is equal to minus 12,
B是-1
B is going to be equal to negative 1.

What two numbers multiply to give negative 12,

but you put together you add together, you get negative 1?

There you got it. I reckon you’re getting a 4 and 3, somewhere there,

but it’s negative 4 and positive 3, or negative 3 and positive 4?

Ok, it’s gonna be a negative 4 and a positive 3.

Because these multiply to give negative 12,
3减去4等于-1
but 3 take away 4 is negative 1.

Ok, so we flip the, these two numbers here, so it becomes 4 and negative 3.

We put them over this coefficient of 6, 6 of 6.

So x can be equal to what?
x可以是2/3 4/6化简后是2/3
X could be equal to 2/3. Let’s simplify that 2/3.
x也可以是-1/2
Or x could be equal to negative 1/2.

Alright. So that’s our really simple way of doing that.

Tell us what you think of this.

Hopefully you enjoyed this video.

Hopefully it was…well, hopefully it was informative.

Anyway, thanks for watching. See you next time. Bye.

sh

Cecilia