Quadratic Equation with Complex Solutions Worksheets

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Printable complex numbers worksheets:
Add & Subtract Complex Numbers
Multiply Complex Number
Rationalize Complex Number
Operations with Complex Numbers
Quadratic Equation with Complex Solutions

Examples, solutions, videos, and worksheets to help Algebra II students learn how to solve quadratic equations with real coefficients that have complex solutions. How to use the discriminant to analyze quadratic equations and recognize when the quadratic formula gives complex solutions.

How to use the Discriminant to Analyze Quadratic Equations?

The discriminant is the part of the quadratic formula that lies under the radical sign: b² - 4ac. It tells us about the nature of the roots of a quadratic equation of the form ax² + bx + c = 0.

If the discriminant is positive (b² - 4ac > 0):
The quadratic equation has two distinct real roots.
The graph of the quadratic function intersects the x-axis at two distinct points.
If the discriminant is zero (b² - 4ac = 0):
The quadratic equation has one repeated real root.
The graph of the quadratic function touches the x-axis at exactly one point.
If the discriminant is negative (b² - 4ac < 0):
The quadratic equation has two complex roots.
The graph of the quadratic function does not intersect the x-axis.

The following diagram shows how the discriminant of a quadratic equation tells what types of roots the equation has.

Have a look at this video if you need to review how to solve a quadratic equation with complex solutions.

Quadratic Formula - Complex Solutions

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Quadratic Equation with Complex Solutions Worksheets

How to use the Discriminant to Analyze Quadratic Equations?

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