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 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

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

Back

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

Front

Calculate the discriminant for the equation y = x² + 4x + 4.

Back

D = 4² - 4(1)(4) = 16 - 16 = 0.

Front

What is the significance of the discriminant in relation to the graph of a quadratic function?

Back

The discriminant helps determine the number of x-intercepts (real solutions) of the quadratic function's graph.

Front

For the quadratic equation -3x² - 5x + 15 = 7, what is the discriminant and how many solutions does it have?

Back

D = 121, which indicates 2 solutions.

Front

What is the formula for calculating the discriminant?

Back

D = b² - 4ac.

Front

If a quadratic equation has a discriminant of 0, what can be said about its vertex?

Back

The vertex of the parabola touches the x-axis at the root, indicating the minimum or maximum point.