Understanding the Discriminant in Quadratic Equations

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

• Two imaginary solutions

• Two real solutions

• One real solution

• No real solutions

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

• One

• None

• Two

• Three

What is the formula for the discriminant in a quadratic equation?

• b^2 + 4ac

• b^2 - 4ac

• a^2 - 4bc

• a^2 + 4bc

In the equation x^2 + 4x + 7 = 0, what are the values of a, b, and c?

• a = 1, b = 4, c = 7

• a = 4, b = 1, c = 7

• a = 7, b = 4, c = 1

• a = 1, b = 7, c = 4

For the equation x^2 + 4x + 7 = 0, what is the value of the discriminant?

• -12

• -16

• 16

• 12

How many imaginary solutions does the equation x^2 + 4x + 7 = 0 have?

• One

• None

• Two

• Three

In the equation x^2 + 3x - 8 = 0, what is the value of the discriminant?

• 41

• -41

• 32

• -32

How many real solutions does the equation x^2 + 3x - 8 = 0 have?

• None

• Three

• One

• Two

For the equation x^2 + 6x + 9 = 0, what is the value of the discriminant?

• 9

• 0

• 36

• 18

How many real solutions does the equation x^2 + 6x + 9 = 0 have?

• None

• Three

• One

• Two