Discriminant Practice

Front

What is the discriminant of a quadratic equation?

Back

The discriminant is a value calculated from the coefficients of a quadratic equation in the form ax² + bx + c, given by the formula D = b² - 4ac. It determines the nature of the roots.

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 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

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

How do you find the discriminant of the quadratic equation 2x² + 4x + 2?

Back

For the equation 2x² + 4x + 2, a = 2, b = 4, c = 2. The discriminant D = b² - 4ac = 4² - 4(2)(2) = 16 - 16 = 0.

Front

What are the values of a, b, and c in the quadratic equation 3x² - 6x + 9?

Back

In the equation 3x² - 6x + 9, a = 3, b = -6, c = 9.

Front

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

Back

A discriminant of 25 is positive, indicating that the quadratic equation has 2 distinct real solutions.

Front

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

Back

The formula for the discriminant D of a quadratic equation ax² + bx + c is D = b² - 4ac.

Front

For the quadratic equation x² - 4x + 4, what is the discriminant?

Back

For the equation x² - 4x + 4, a = 1, b = -4, c = 4. The discriminant D = (-4)² - 4(1)(4) = 16 - 16 = 0.

Front

What type of solutions does the quadratic equation 5x² + 10x + 5 have?

Back

The equation 5x² + 10x + 5 has a discriminant of 0, indicating it has exactly one real solution.