Answer:
1) Methods:
- Quadratic formula.
- Factorization.
- Completing the square.
2) If the determinant is less than zero () then there are two roots that are complex conjugates.
Step-by-step explanation:
Methods:
- Quadratic formula
Given the quadratic equation in Standard form , you can solve it with the quadratic formula:
- Factorization
You must find two expression that when you multply them, you get the original quadratic equation. For example:
Find two number whose sum is 6 and whose product is 8. These are 2 and 4. Then:
When you make the multiplication indicated in , you obtain
- Completing the square
Given the quadratic equation in Standard form ,, you must turn it into:
Where:
Once you get that form, you must solve for <em>x</em>.
You can predict if the quadratic function will have a complex solution with the determinant:
If then there are two roots that are complex conjugates.