Imaginary Numbers

What is the discriminant of the following equation?

 $x^2-6x+9=0$  

You compute the discriminant and you get the number -77. What does this mean?

• The quadratic has two real roots.

• The quadratic has one real root.

• The quadratic has zero real roots.

Simplify the square root:

 $\sqrt{-20}$  

•  $2\sqrt{5}$  

•  $-2\sqrt{5}$  

•  $2\sqrt{5}i$  

Simplify the square root:

 $\sqrt{-50}$  

•  $5\sqrt{2}i$  

•  $2\sqrt{5}i$  

•  $-2\sqrt{5}$  

•  $-5\sqrt{2}$  

Determine the value of the discriminant and name the nature of the solution for the following:
x² + 2x - 63
Remember:  b² - 4ac

• 256 - 2 reals - Rational
• √(-256 - 2 imaginary solutions
• √(137) - 2 reals - Irrational
• 123 - 2 reals - Rational

What does the discriminant tell us?

• The maximum or minimum
• The y-intercept
• The number and type of solutions
• The axis of symmetry

Find the discriminant of the quadratic equation:
2x² + 10x - 15 = 0

• 25
• -20
• 220
• 92

• 1

• i

• -1

• -i

Solve using the quadratic formula:
3x²-30x+75 = -81

• x = 5 ±3i√3
• x = 5 ±⅓i
• x = 5 ±9i√3
• x = 5 ±3i

Write $\sqrt{-192}$  in simplest form.

•  $8i\sqrt{3}$  

• 8i + 3

•  $4i\sqrt{12}$   

•  $4i+\sqrt{12}$