Determining Real and Imaginary Solutions with the Discriminant

This video tutorial explains how to calculate the discriminant of a quadratic equation and its significance in determining the number and type of solutions. It covers the quadratic formula and provides examples of equations with two real solutions, one real solution, and two imaginary solutions. The video also demonstrates how to use the quadratic formula to confirm the solutions and discusses the relationship between the discriminant and the nature of the solutions.

What is the discriminant in a quadratic equation?

• 2a

• The coefficient of x

• The constant term

• b^2 - 4ac

If the discriminant is greater than zero, how many real solutions does the quadratic equation have?

• One

• Infinite

• None

• Two

Calculate the discriminant for the equation x^2 + 4x - 7 = 0 when a=1, b=4, c=-7.

• 16

• 0

• 28

• 44

What are the solutions for the equation x^2 + 4x - 7 = 0?

• 1 ± √11

• 1 ± √44

• -2 ± √44

• -2 ± √11

For the equation x^2 - 6x + 9 = 0, what does a discriminant of zero indicate about the solutions?

• Two imaginary solutions

• One real solution

• No real solutions

• Two real solutions

Using factoring, what is the solution for x in the equation x^2 - 6x + 9 = 0?

• x = 6

• x = 0

• x = 9

• x = 3

What is the discriminant of the equation 2x^2 + 5x + 8 = 0?

• 25

• -39

• 64

• 0

What type of solutions does the equation 2x^2 + 5x + 8 = 0 have?

• No real solutions

• Two imaginary solutions

• One real solution

• Two real solutions

What does a negative discriminant indicate about the nature of the solutions in a quadratic equation?

• Two real solutions

• One real solution

• No real solutions

• Two imaginary solutions

For the equation 2x^2 + 5x + 8 = 0, what are the imaginary solutions?

• -1.25 ± 1.56i

• 1.25 ± 1.56i

• -1.25 ± 1.25i

• 1.25 ± 1.25i