Unit 3 Lesson 16-18 Practice

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 of ax^2 + bx + c. It is given by the formula D = b^2 - 4ac. The Discriminant helps determine the nature of the roots of the equation.

Front

What does a Discriminant of 0 indicate about the roots of a quadratic equation?

Back

A Discriminant of 0 indicates that the quadratic equation has exactly one real root, also known as a repeated or double root.

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 negative Discriminant indicate about the roots of a quadratic equation?

Back

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

Front

Back

Front

Back

Front

How do you determine the number of real roots from the Discriminant?

Back

You can determine the number of real roots by evaluating the Discriminant: If D > 0, there are 2 real roots; if D = 0, there is 1 real root; if D < 0, there are no real roots.

Front

What is the formula for calculating the Discriminant?

Back

The formula for calculating the Discriminant is D = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c.

Front

If a quadratic equation has a Discriminant of 36, how many real roots does it have?

Back

It has 2 distinct real roots.

Front

If a quadratic equation has a Discriminant of 256, how many real roots does it have?

Back

It has 2 distinct real roots.