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, also known as a repeated or double 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 two complex (imaginary) solutions.

Front

Given the quadratic equation 4x² - 8x - 3 = 0, identify a, b, and c.

Back

a = 4, b = -8, c = -3.

Front

If the discriminant is equal to -2, how many solutions are there?

Back

There are 2 imaginary solutions.

Front

What does the discriminant tell us about the nature of the roots of a quadratic equation?

Back

The discriminant tells us the number and type of solutions (real or imaginary) of the quadratic equation.

Front

If the discriminant is positive, what can we conclude about the roots?

Back

If the discriminant is positive, there are two real solutions.

Front

If the discriminant is negative, what can we conclude about the roots?

Back

If the discriminant is negative, there are two imaginary solutions.

Front

What is the formula for calculating the discriminant?

Back

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