Use the discriminant* to identify the types of roots
![Picture](/uploads/1/1/5/3/11531538/7914759.png)
The discriminant is a number that can be calculated from any quadratic equation. A quadratic equation can be written as: ax^2 + bx + c. The discriminant would be b^2 - 4ac. Note: you will remember that b^2 - 4ac is a part of the quadratic formula. The discriminant of a quadratic equation will provide information on the nature of the root/s. For example:
The discriminant of this equation would be: (4)^2 - (4 x 1 x 3) = 16 - 12 = 4.
There are 3 cases:
The discriminant of this equation would be: (4)^2 - (4 x 1 x 3) = 16 - 12 = 4.
There are 3 cases:
- the discriminant > 0
- the discriminant = 0
- the discriminant < 0
Case 1. the discriminant > 0
![Picture](/uploads/1/1/5/3/11531538/9031114.png)
A positive discriminant would have 2 real roots. An example of a graph of a quadratic equation with a positive discriminant is shown on the left.
![Picture](/uploads/1/1/5/3/11531538/3464622.png)
This is another graph of a quadratic equation with a positive discriminant. Note: it has 2 intercepts on the x axis, and therefore 2 real solutions.
Case 2. the discriminant = 0
![Picture](/uploads/1/1/5/3/11531538/4525926.png)
If the discriminant is equal to 0, then there is only one real solution. An example of a graph of a quadratic equation with a discriminant = 0 is shown on the left.
![Picture](/uploads/1/1/5/3/11531538/4449372.png)
This is another graph of a quadratic equation with a discriminant = 0. Note: it has only 1 intercepts on the x axis, and therefore only 1 real solution.
Case 3. the discriminant < 0
![Picture](/uploads/1/1/5/3/11531538/7284245.png)
A negative discriminant would have no real roots. An example of a graph of a quadratic equation with a negative discriminant is shown on the left.
![Picture](/uploads/1/1/5/3/11531538/1096247.png)
This is another graph of a quadratic equation with a discriminant < 0. Note: it has no intercepts on the x axis, and therefore no real solutions.