Quadratic Equations with Complex Roots

When the discriminant of a quadratic equation is negative, the equation has complex conjugate roots.

Quadratic Formula

Discriminant

Complex Conjugate Roots

Example: Complex Roots

Sum and Product of Complex Roots

Example: Finding Quadratic from Roots

Practice Problems

1. Find the roots of .
2. If one root of is , find .
3. Find the quadratic equation with roots and .
4. Prove that the product of complex conjugate roots is always a positive real number.