ALG2 3.4 - Finding the Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac. It determines the nature of the roots of the quadratic equation.

Front

How do you calculate the discriminant for the quadratic equation ax² + bx + c = 0?

Back

The discriminant is calculated using the formula D = b² - 4ac.

Front

What does a positive discriminant indicate about the solutions of a quadratic equation?

Back

A positive discriminant indicates that the quadratic equation has two distinct real solutions.

Front

What does a discriminant of zero indicate about the solutions of a quadratic equation?

Back

A discriminant of zero indicates that the quadratic equation has exactly one real solution (a repeated root).

Front

What does a negative discriminant indicate about the solutions of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has no real solutions, but two complex solutions.

Front

Given the quadratic equation -8x² + 6x - 4 = 0, what is the discriminant?

Back

The discriminant is -92, indicating no real solutions.

Front

For the equation 3x² + 8x = 0, what is the discriminant?

Back

The discriminant is 64, indicating two distinct real solutions.

Front

In the equation 9x² + 4x - 6 = -5x + 8, what are the values of a, b, and c in standard form?

Back

a = 9, b = 9, c = -14.

Front

What is the discriminant of the equation -5x² - 6 = 0?

Back

The discriminant is -120, indicating no real solutions.

Front

In the equation 8x² + 3x - 6 = 3x, what are the values of a, b, and c in standard form?

Back

a = 8, b = 0, c = -6.