Discriminant & Roots

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 b² - 4ac.

Tags

CCSS.HSA-REI.B.4B

Front

How do you determine the number of solutions from the discriminant?

Back

If the discriminant is positive, there are 2 real solutions. If it is zero, there is 1 real solution. If it is negative, there are 2 imaginary solutions.

Tags

CCSS.HSA-REI.B.4B

Front

What is the formula for the discriminant?

Back

b² - 4ac

Tags

CCSS.HSA-REI.B.4B

Front

Given the quadratic equation 4x² + 6x - 4 = 0, what is the discriminant and how many solutions does it have?

Back

Discriminant: 100, Solutions: 2 Solutions.

Tags

CCSS.HSA-REI.B.4B

Front

Given the quadratic equation -8x² + 6x - 4 = 0, what is the discriminant and how many solutions does it have?

Back

Discriminant: -92, Solutions: No Solutions (2 imaginary solutions).

Tags

CCSS.HSA-REI.B.4B

Front

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

Back

Discriminant: 121, Solutions: 2 Solutions.

Tags

CCSS.HSA-REI.B.4B

Front

Given the quadratic equation 3x² + 3x + 4 = -3, what is the discriminant and how many solutions does it have?

Back

Discriminant: -75, Solutions: No Solutions (2 imaginary solutions).

Tags

CCSS.HSA-REI.B.4B

Front

What does a positive discriminant indicate about the roots of a quadratic equation?

Back

A positive discriminant indicates that the quadratic equation has 2 distinct real roots.

Tags

CCSS.HSA-REI.B.4B

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 1 real root (a repeated root).

Tags

CCSS.HSA-REI.B.4B

Front

What does a negative discriminant indicate about the roots of a quadratic equation?

Back

A negative discriminant indicates that the quadratic equation has 2 complex (imaginary) roots.

Tags

CCSS.HSA-REI.B.4B