Throwback Thursday :D

Solve radical equations

100

Solve \sqrt(x) = 5

x = 25

200

Solve \sqrt(x-3) = 9

x = 84

300

Solve \cbrt(x - 12) = 5

x = 137

400

Solve \sqrt(2x+1) - 4 = -7. 

no solution :3

500

Solve x + 1 = \sqrt(3x + 13)

x = 4

Complex Numbers

100

Evaluate i⁴

1

200

Evaluate i¹³

i

300

Simplify (1 + 5i) + (3 - 2i). Write your answer in a+bi form.

4 + 3i

400

Simplify (8 - 3i) - (2 - 4i). Write your answer in a+bi form.

6 + i

500

Simplify (3 + 2i)(2 - 3i). Write your answer in a+bi form.

12 - 5i

Quadratic Equations

100

Label a, b, and c: 7x² - x + 3 = 0

a = 7

b = -1

c = 3

200

Use the discriminant to determine the types of solutions the following quadratic has:

10x² - 5x + 2 = 0

2 non-real solutions (2 imaginary solutions)

300

Use the discriminant to determine the types of solutions the following quadratic has:

3x² + 6x + 3 = 0

1 real solution

400

Find all complex solutions for the following equation:

x² - 3x + 4 = 0

x = \frac(3 ± i \sqrt(7))(2)

500

Find all complex solutions to the following equation:

0.5x² - 0.6x + 0.5 = 0

\frac(3 ± 4i)(5)

Miscellaneous

100

Write \cbrt(x⁵) in exponential form.

x^\frac(5)(3)

200

Evaluate (-64)^\frac(2)(3)

16

300

What is the domain for the function f(x)=\frac( x + 1 )( 2x - 3 )?

all real numbers except 3/2

400

Consider the function: p(x)= x⁷ + 5x⁶ - 3x² - 1. As x approaches positive infinity, what value does p(x) approach?

infinity (degree is odd + leading coefficient is positive)

500

The function f(x) approaches positive infinity as x approaches positive infinity. The zeros of the function are -1, 2, and 4. 

answers may vary