4. Solving Quadratic equations in complex numbers

Solving Quadratic equations in complex numbers

We can solve quadratic equations with complex coefficients using the quadratic formula. If the discriminant is zero, the equation has one repeated root. If all the coefficients are real, the root will be real. A general quadratic with complex coefficients can have any combination of real and nonreal roots.

The Quadratic Formula is   The expression under the radical, is called the discriminant. You can use the discriminant to determine the number and type of solutions an equation has.

Using the discriminant, we identify the three different cases of quadratic equations as follows.

Solving Equations with Different Types of Solutions

4. Nonreal Quadratic Equations with Real Negative Discriminants