Finding the Discriminant

Front

What is the formula for calculating the discriminant of a quadratic equation?

Back

The discriminant (d) is calculated using the formula d = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.

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 -2x² - x - 1 = 0, what is the discriminant?

Back

The discriminant is -7.

Front

If a quadratic function has a discriminant of 25, how many solutions does it have?

Back

It has 2 real solutions.

Front

What is the discriminant of the quadratic equation 6x² - 2x - 3 = 0?

Back

The discriminant is 76.

Front

How can you determine the nature of the roots of a quadratic equation using the discriminant?

Back

By evaluating the discriminant: if d > 0, there are 2 real solutions; if d = 0, there is 1 real solution; if d < 0, there are 2 complex solutions.

Front

What is the discriminant of the quadratic equation represented by d = (-5)² - 4(2)(-2)?

Back

The function is 2x² - 5x - 2.

Front

What is the significance of the coefficients a, b, and c in the context of the discriminant?

Back

The coefficients a, b, and c are used in the discriminant formula d = b² - 4ac to determine the nature of the roots of the quadratic equation.