Finding the Discriminant

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is a value that determines the nature of the roots of a quadratic equation, given by the formula b² - 4ac.

Front

Calculate the discriminant for the equation: 2x² + 3x + 1 = 0.

Back

The discriminant is 3² - 4(2)(1) = 9 - 8 = 1.

Front

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

Back

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

Front

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

Back

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

Front

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

Back

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

Front

Given A = 1, B = -4, and C = 4, find the discriminant.

Back

The discriminant is (-4)² - 4(1)(4) = 16 - 16 = 0.

Front

What is the formula for the discriminant?

Back

The formula for the discriminant is b² - 4ac.

Front

If the discriminant is -32, what can be said about the roots of the quadratic equation?

Back

The roots are complex and not real.

Front

Find the discriminant for the equation: -5x² - 6 = 0.

Back

The discriminant is 0² - 4(-5)(-6) = 0 - 120 = -120.

Front

What is the significance of the discriminant in the quadratic formula?

Back

The discriminant helps determine the number and type of solutions for the quadratic equation.