Discriminant in Quadratic Formula
In this lesson, we learn about the discriminant in the quadratic formula and how it can be used to determine what types of solutions a quadratic equation has. The discriminant is the part underneath the square root symbol in the quadratic formula, and it can be greater than zero, equal to zero, or less than zero. If it's greater than zero, there are two real solutions; if it's equal to zero, there is one real solution; and if it's less than zero, there are two complex solutions. The discriminant can be useful in graphing and determining the number and types of solutions of a quadratic equation without actually solving for them.
Defines the discriminant and how to use it to find what types of solutions a quadratic equation has.
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- What is the discriminant in the quadratic formula?
- What happens if the discriminant, or b^2 - 4ac, is > 0?
- What happens if the discriminant, or b^2 - 4ac, is < 0?
- What happens if the discriminant, or b^2 - 4ac, equals 0?
- When do you get two real solutions when solving a quadratic equation using the quadratic formula?
- When do you get two complex or imaginary solutions when solving a quadratic equation using the quadratic formula?
- When do you get only one solution when solving a quadratic equation using the quadratic formula?
- What are complex conjugates?
- How can you use the discriminant to determine the number and types of solutions of 2x^2 - 3x + 4 = 0?
- How can you use the discriminant to determine the number and types of solutions of 4x^2 - 12x = -9?
- How can you use the discriminant to determine the number and types of solutions of 8m^2 - 2m - 7 = 0?
- What happens if the discriminant, or b^2 - 4ac, is a perfect square?
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Staff Review
This lesson explains the three scenarios that can occur when solving a quadratic equation -- you can get 2 real solutions, 1 real solution, or 2 complex solutions. You can determine which of these will occur based on the discriminant of the quadratic equation, b^2 - 4ac. This is a great synopsis of the different things that can happen when solving a quadratic equation.
