$$x = 2$$, restriction $$x \neq 1$$

Question 1

Which of the following points is located in Quadrant II of the rectangular coordinate system?

Accepted Answer

$$(-3, 2)$$

Question 2

Solve the equation $$3(2 - 5x) = 4x + 25$$ for $$x.$$

Accepted Answer

$$x = -1.5$$

Question 3

Which of the following is the standard form of a quadratic equation?

Accepted Answer

$$ax^2 + bx + c = 0$

Question 4

What is the solution set for the equation $$x + 5 = x + 2 + 3$$?

Accepted Answer

All real numbers

Question 5

Simplify $$i^{85}.$$

Accepted Answer

$$i$$

Question 6

Find the sum $$(4 + 8i) + (2 + 3i)$$ and express your answer in standard form.

Accepted Answer

$$6 + 11i$$

Question 7

What is the product of $$(2 + 3i)(2 - 3i)$$?

Accepted Answer

$$13$$

Question 8

Divide and express in standard form: $$\frac{6 + i}{4 - 2i}.$$

Accepted Answer

$$1 + \frac{2}{5}i$$

Question 9

Which of the following best describes the discriminant $$b^2 - 4ac$ of the quadratic equation x^2$ + 8x + 16 = 0$$?

Accepted Answer

Zero, one real solution

Question 10

Solve the quadratic equation $$2x^2 + 7x + 6 = 0$ by factoring.

Accepted Answer

$$x = -2, x = -1.5$$

Question 11

Which of the following intervals represents the solution set to $$2x + 12 \u003e 19$$?

Accepted Answer

$$(3.5, \infty)$$

Question 12

Solve the rational equation $$\frac{2x+4}{x-1} = 5$$ and state any restrictions.

Accepted Answer

$$x = 2$$, restriction $$x 
eq 1$$

Question 13

Which of the following is the correct interval notation for the set $$\{x | 0 \u003c x \u003c 5\}$$?

Accepted Answer

$$(0, 5)$$

Question 14

Solve the equation $$\frac{x}{4} + \frac{1}{6} = \frac{x}{3}$$ and categorize the equation.

Accepted Answer

Conditional equation, $$x = 2$$

Question 15

Which of the following is the correct standard form for the quadratic equation $$-4x^2 + x = 8$?

Accepted Answer

$$-4x^2 + x - 8 = 0$

Question 16

If $$i = \sqrt{-1}$$, what is $$i^{1003}$$?

Accepted Answer

$$i$$

Question 17

Solve the quadratic equation $$x^2 + 3x - 5 = 0$ by completing the square.

Accepted Answer

$$x = \frac{-3 \pm \sqrt{9 + 20}}{2}$$

Question 18

Which of the following is the correct solution for $$2x^2 - 16 = 0$ using the square root property?

Accepted Answer

$$x = \pm 2\sqrt{2}$$

Question 19

A chemical reaction is modeled by the equation $$3x^2 + 4x + 1 = 0$. Using the quadratic formula, what are the solutions for x$?

Accepted Answer

$$x = \frac{-4 \pm 2}{6}$$

College Algebra: Equations, Inequalities, and Complex Numbers

Study Guide - Practice Questions