Discriminant

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 of the roots of the equation.

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 two complex (imaginary) roots.

Front

How do you calculate the discriminant for the quadratic equation ax² + bx + c = 0?

Back

The discriminant is calculated using the formula D = b² - 4ac.

Front

If the discriminant is 0, how many solutions does the quadratic equation have?

Back

The quadratic equation has one real solution.

Front

What is the relationship between the x-intercepts and the roots of a quadratic equation?

Back

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

Front

True or False: The solution, root, x-intercept, and zero of a quadratic equation are all the same thing.

Back

True.

Front

Solve the quadratic equation 2x² + 2x - 12 = 0 using the quadratic formula.

Back

x = 2, -3.

Front

Given the quadratic equation x² - 6x + 9 = 0, what is the discriminant and how many solutions does it have?

Back

The discriminant is 0, and it has 1 real solution.