Quadratic Formula with Complex Solutions & Discriminate

Front

What is the quadratic formula?

Back

x = (-b ± √(b² - 4ac)) / (2a)

Front

What does the discriminant (D) represent in a quadratic equation?

Back

The discriminant determines the nature of the roots of the quadratic equation.

Front

What is the formula for the discriminant?

Back

D = b² - 4ac

Front

If the discriminant is positive, what can be said about the solutions?

Back

There are two distinct real solutions.

Front

If the discriminant is zero, what can be said about the solutions?

Back

There is exactly one real solution (a repeated root).

Front

If the discriminant is negative, what can be said about the solutions?

Back

There are two complex (imaginary) solutions.

Front

What does it mean if the discriminant is a perfect square?

Back

The solutions are rational numbers.

Front

Calculate the discriminant for the equation: 2x² + 4x + 2 = 0.

Back

D = 4² - 4(2)(2) = 16 - 16 = 0.

Front

For the equation x² + 5x + 6, what is the discriminant and the nature of the solutions?

Back

D = 5² - 4(1)(6) = 25 - 24 = 1; two distinct real solutions.

Front

What is the discriminant of the equation 3x² - 6x + 5?

Back

D = (-6)² - 4(3)(5) = 36 - 60 = -24; two complex solutions.