Quadratic Formula and Discriminant

Rational Solutions

Irrational Solutions

Imaginary Solutions

Multiple Choice

Solve Using the Quadratic Formula
 x² + 4x - 40 = -8

• -10 & -4
• -4 & 10
• -8 & 4
• 8 & -4

Multiple Choice

Determine the values of
a, b, and c for
the quadratic equation: 
4x² – 8x = 3

• a = 4, b = -8, c = 3
• a = 4, b =-8, c =-3
• a = 4, b = 8, c = 3
• a = 4, b = 8, c = -3

Multiple Choice

What does the discriminant tell us?

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

Multiple Choice

The formula to determine how many solutions a quadratic equation is called the discriminant which is...

• aX² + bX + c

• b - 4ac

• b² - 4ac

• b² + 4ac

Multiple Choice

If the discriminant is negative, you will have....

• two real solutions

• two irrational solutions

• no real solution

• one solution

Multiple Choice

Use the discriminant to determine the number of solutions the following quadratic equation has.

6x² − 2x − 3 = 0

• 76 Two Solutions

• 29 Two Solutions

• 68 Two Solutions

• none of these

Multiple Choice

Solve using the Quadratic Formula:
$$5x^2+3x-1=0$$

• $$x=\frac{3\pm\sqrt{29}}{5}$$  

• $$x=\frac{8}{5}\ or\ x=-\frac{2}{5}$$  

• $$x=\frac{-3\pm\sqrt{29}}{10}$$  

• No real solutions

Multiple Choice

Solve by using a method of your choice:

k² − 12k + 23 = 0

• {6 + √13, 6 - √13}

• {-6 + √13, -6 - √13}

• {6 + √59, 6 - √59}

• {-6 + √59, -6 - √59}

Multiple Choice

Simplify √-4

• 2i
• -2i
• 2
• 4i

Multiple Choice

$$For\ 2x^2\ -\ 4x\ +\ 3\ =\ 0,\ which\ is\ correct?$$  

• $$\frac{4\ \pm\sqrt{-16\ -4\left(2\right)\left(3\right)}}{2\left(2\right)}$$  

• $$\frac{-4\ \pm\sqrt{16\ -4\left(2\right)\left(3\right)}}{2\left(2\right)}$$  

• $$\frac{4\pm\sqrt{16-4\left(2\right)\left(3\right)}}{4}$$  

• $$\frac{4\pm\sqrt{40}}{4}$$  

Multiple Choice

Solve

$$2x^2+4x\ +10=0$$  

Simplify answers

• $$-4\ \pm8i$$  

• $$-1\pm2i$$  

• $$\frac{-4\ \pm8i}{4}$$  

• $$\pm8i$$