Discriminant

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac in the quadratic formula, 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 discriminant of zero indicate about the roots of a quadratic equation?

Back

A discriminant of zero indicates that the quadratic equation has exactly one real 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

Calculate the discriminant for the quadratic equation x² + 7x + 13.

Back

The discriminant is -3, indicating 2 imaginary roots.

Front

In the quadratic equation y = ax² + bx + c, what do a, b, and c represent?

Back

a is the leading coefficient, b is the coefficient of x, and c is the constant term.

Front

True or False: The quadratic formula can be used to solve any quadratic equation, regardless of whether it can be factored.

Back

True.

Front

If a quadratic function has a discriminant of -3, how many x-intercepts does it have?

Back

0 x-intercepts.

Front

If a quadratic function has a discriminant of 4, how many x-intercepts does it have?

Back

2 x-intercepts.

Front

What is the formula for the discriminant?

Back

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