The Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is a value calculated from the coefficients of a quadratic equation in the form ax² + bx + c. It is given by 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 zero discriminant indicate about the solutions of a quadratic equation?

Back

A zero discriminant 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

Calculate the discriminant for the quadratic equation 4x² + 6x - 4 = 0.

Back

D = b² - 4ac = 6² - 4(4)(-4) = 36 + 64 = 100.

Front

Calculate the discriminant for the quadratic equation -2x² - x - 1 = 0.

Back

D = b² - 4ac = (-1)² - 4(-2)(-1) = 1 - 8 = -7.

Front

If the discriminant of a quadratic equation is 0, how many real solutions does it have?

Back

It has exactly one real solution.

Front

If the discriminant of a quadratic equation is positive, how many real solutions does it have?

Back

It has two distinct real solutions.

Front

If the discriminant of a quadratic equation is negative, what type of solutions does it have?

Back

It has two complex solutions.

Front

What is the formula for calculating the discriminant?

Back

D = b² - 4ac.