Equations with Imaginary Number Solutions

Determine the value of the discriminant and name the nature of the roots for the following:
x² + 7x + 13
Remember:  b² - 4ac

• 400, 2 real root 

• 0, 1 real root with a multiplicity of 2

• -400, 2 imaginary roots

• -3, 2 imaginary roots

The discriminant is

• aX²  + bX  +  c

• b - 4ac

• b² - 4ac

• b² + 4ac

If the discriminant is negative, then the solution will be

• one real solution

• two real solutions

• two imaginary solutions

• one imaginary solution

What type of numbers are involved when a quadratic equation has complex solutions?

• Natural numbers

• Imaginary numbers

• Rational numbers

• Whole numbers

If a quadratic equation has solutions expressed as a + bi, what do 'a' and 'bi' represent?

• The x-intercepts of the graph

• The roots of the equation

• The coefficients of the equation

• The real and imaginary parts of the solution

Which of the following indicates that a quadratic equation has complex solutions?

• The discriminant is greater than zero

• The discriminant is equal to zero

• The coefficients are all positive

• The discriminant is less than zero

In which field might you encounter quadratic equations with complex solutions?

• Literature

• History

• Electrical engineering

• Biology

Perform the operations using the given complex numbers. Select the correct value for each hotspot.

c

d

2

15

-2

4

-5

-4

Perform the operation using the given complex numbers.

d

f

2

4

-5

-12

-4

5

-2

When a quadratic equation has a discriminant that is NEGATIVE, what type of solution does it have?

• two imaginary solutions

• two real solutions

• one real solution, one imaginary solution

• no solution

• one real solution