Kotik Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is a value calculated from the coefficients of a quadratic equation, given by the formula b² - 4ac.

Front

How do you calculate the discriminant for the equation 6x² − 2x − 3 = 0?

Back

For the equation 6x² − 2x − 3, a = 6, b = -2, c = -3. The discriminant is (-2)² - 4(6)(-3) = 4 + 72 = 76.

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 (a repeated 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 no real solutions (the solutions are complex).

Front

What is the formula for the discriminant?

Back

The formula for the discriminant is b² - 4ac.

Front

Use the discriminant to determine the number of solutions for -2x² − x − 1 = 0.

Back

For -2x² − x − 1, a = -2, b = -1, c = -1. The discriminant is (-1)² - 4(-2)(-1) = 1 - 8 = -7, indicating no solutions.

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

Solve the quadratic equation x² + 4x - 40 = -8 using the quadratic formula.

Back

Rearranging gives x² + 4x - 32 = 0. Using the quadratic formula, x = (-b ± √(b² - 4ac)) / 2a, we find x = -8 and x = 4.

Front

What is the relationship between the discriminant and the vertex of a parabola?

Back

The discriminant does not directly determine the vertex, but it indicates how many times the parabola intersects the x-axis.