In this video, you will learn how to solve
the quadratic inequality using a number line
Suppose we have a quadratic inequality x^2-7x+12>0
First, factorise the quadratic expression
into 2 brackets
Each bracket is a number, let's call them
A and B
We have two numbers, when they multiply together,
the answer is greater than 0
So, these 2 numbers must be either both positive
or both negative
Next, We always let both brackets be greater
than 0, and then solve the inequalities
After solving them, we draw both range of
x on the number line
The number line x>3 represents the region
that will make x-3 to be positive
While the number line x>4 represents the region
that will make x-4 to be positive
All other regions will make x-3 or x-4 to
be negative
Since this quadratic expression is greater
than 0, we choose the regions that are both
positive or both negative
The solution for this quadratic inequality
is x4
What about the quadratic inequality x^2-7x+12<0?
First, we also factorise it into two brackets
A and B
Since we want the expression to be less than
0, A and B must be one positive and one negative
Letting both A and B to be greater than 0,
we find the range of x
Then, plot the number line again and this
time, choose the negative regions since we
want the expression to be less than 0
Hence, the solution is x between 3 and 4
