MATHEMATICS 9
Topic: Quadratic Equations and Discriminants
Learning Objective:
At the end of this topic , students are able to:
1. Know the essential concepts of dealing with quadratic equations using quadratic
formula
2. Determine the number of solutions/roots of a quadratic equation using Discriminant
QUADRATIC EQUATIONS AND QUADRATIC FORMULA
Quadratic Equation
-An equation where the highest exponent of the variable (usually "x") is a square ( 2).
So it will have something like x2
But not x3 etc.
A Quadratic Equation is usually written ax2 + bx + c = 0
Example: 2x2 + 5x − 3 = 0
*The exponent 2 makes it quadratic
a, b and c are known values. a can't be 0.
"x" is the variable or unknown (we don't know it yet).
Here are some examples:
2x2 + 5x + 3 = 0 In this one a=2, b=5 and c=3
x2 − 3x = 0 This one is a little more tricky:
Where is a? Well a=1, as we don't usually write "1x2"
b = −3
And where is c? Well c=0, so is not shown.
5x − 3 = 0 Oops! This one is not a quadratic equation: it is missing x2
(in other words a=0, which means it can't be quadratic)
As we saw before, the Standard Form of a Quadratic Equation is
Topic: Quadratic Equations and Discriminants
Learning Objective:
At the end of this topic , students are able to:
1. Know the essential concepts of dealing with quadratic equations using quadratic
formula
2. Determine the number of solutions/roots of a quadratic equation using Discriminant
QUADRATIC EQUATIONS AND QUADRATIC FORMULA
Quadratic Equation
-An equation where the highest exponent of the variable (usually "x") is a square ( 2).
So it will have something like x2
But not x3 etc.
A Quadratic Equation is usually written ax2 + bx + c = 0
Example: 2x2 + 5x − 3 = 0
*The exponent 2 makes it quadratic
a, b and c are known values. a can't be 0.
"x" is the variable or unknown (we don't know it yet).
Here are some examples:
2x2 + 5x + 3 = 0 In this one a=2, b=5 and c=3
x2 − 3x = 0 This one is a little more tricky:
Where is a? Well a=1, as we don't usually write "1x2"
b = −3
And where is c? Well c=0, so is not shown.
5x − 3 = 0 Oops! This one is not a quadratic equation: it is missing x2
(in other words a=0, which means it can't be quadratic)
As we saw before, the Standard Form of a Quadratic Equation is
