Hi.
What I'd like to do
now is show you guys
how to find the
roots of an equation,
given x-squared
minus 8x equals 9.
First of all, this is not
in a x plus b y or-- sorry--
a x-squared plus
bx plus c equals 0.
So what we need to do is first,
I need to set this equal to 0
because remember, when
solving for your roots,
the roots are the same
thing as your x-intercepts.
So therefore, you need to
have that set equal to 0.
So what I'm going
to do is I'm just
going to subtract a
9 out of both sides.
And therefore, what I obtain
now is my x-squared minus
8x minus 9 equals 0.
Now it's in a familiar form.
Now I can determine
what my a, b, and c are.
My a is equal to 1, b
is equal to negative 8,
and c is equal to negative 9.
So then, now I can simply go
ahead and do my a times c.
a times c becomes negative
9 and my b is a negative 8.
So I say, what two numbers
multiply to give me negative 9
but add to give me negative 8?
Well, it's either 3
times 3 or 9 times 1.
So yes?
Negative 1 and positive 8--
9.
Say that again.
Negative 1 and positive 9.
But you want to have
a negative 8, though.
That would be a negative 8.
Never mind.
But when you add
them together, you're
going to want to
get a negative 8.
So you had it correct but you're
just going to want to make sure
that's a negative
9 and a positive 1.
So you've just got to make
sure you flip those around.
Therefore, now you have
negative 9 and positive 1
so I just put them in my factor.
So I have x minus 9
times x plus 1 equals 0.
You cannot forget to
have that equal 0.
It's a very big mistake
that a lot of students
will go ahead and
make is they will not
continue to have the equal 0.
Now, using the
zero-product property,
I know that this binomial equals
0 and this binomial equals 0.
So therefore, I say x minus 5
equals 0 and x plus 1 equals 0.
Then you just solve
for your variable.
And that is how you find
the roots of the equation.
