Front

What is the Discriminant in a quadratic equation?

Back

The Discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature and number of solutions of the quadratic equation ax² + bx + c = 0.

Front

What does a positive Discriminant indicate?

Back

A positive Discriminant indicates that the quadratic equation has two distinct real solutions.

Front

What does a Discriminant of zero indicate?

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?

Back

A negative Discriminant indicates that the quadratic equation has no real solutions, but two complex solutions.

Front

How do you calculate the Discriminant for the equation 2x² + 3x - 5 = 0?

Back

The Discriminant is calculated as b² - 4ac = (3)² - 4(2)(-5) = 9 + 40 = 49.

Front

What is the Quadratic Formula?

Back

The Quadratic Formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation.

Front

If the Discriminant is 0, what is the nature of the roots?

Back

The roots are real and equal (or repeated).

Front

What is the Discriminant of the equation x² - 4x + 4 = 0?

Back

The Discriminant is 0, indicating one real solution.

Front

Calculate the Discriminant for the equation 3x² + 6x + 2 = 0.

Back

The Discriminant is b² - 4ac = (6)² - 4(3)(2) = 36 - 24 = 12.

Front

What is the significance of the x-intercept in relation to the roots of a quadratic equation?

Back

The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, which correspond to the real roots of the equation.