What are the methods for solving quadratic equations and what indicators predict that a quadratic function will have a complex solution?

 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 x.

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.

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