Question 1

Which of the following is the correct definition of the discriminant for a quadratic equation $$ax^2 + bx + c = 0$?

Accepted Answer

$$D = b^2$ - 4ac$$

Question 2

Solve the quadratic equation $$x^2 - 5x + 6 = 0$ by factoring.

Accepted Answer

$$x = 2 or$$ $$x = 3$$

Question 3

Which of the following best describes the number and type of solutions for the equation $$x^2 + 4x + 5 = 0$?

Accepted Answer

Two complex solutions

Question 4

Solve the equation $$2x^2 = 18$ using the square root property.

Accepted Answer

$$x = 3 or$$ $$x = -3$$

Question 5

Which of the following is the correct solution to the equation $$x^2 - 6x + 8 = 0$ using the quadratic formula?

Accepted Answer

$$x = 4 or$$ $$x = 2$$

Question 6

Solve the radical equation $$\sqrt{x + 5} = 4.$$

Accepted Answer

$$x = 11$$

Question 7

Solve the equation with rational exponents: $$x^{3/2} = 8$.

Accepted Answer

$$x = 16$$

Question 8

Which of the following is the solution to the linear inequality $$3x - 7 \u003c 2$$?

Accepted Answer

$$x \u003c 3$$

Question 9

A company needs to ensure that the temperature in a storage room stays within 2 degrees of 70°F. Which absolute value inequality models this situation?

Accepted Answer

$$|T - 70| \leq 2$$

Question 10

Solve the absolute value equation $$|2x - 3| = 7.$$

Accepted Answer

$$x = 5 or$$ $$x = -2$$

Question 11

Which of the following is the correct first step in solving the equation $$x^2 + 8x = -15$ by completing the square?

Accepted Answer

Add 15 to both sides

Question 12

Solve the polynomial equation $$x^3$$ - $$4x^2 = 0$ by factoring.

Accepted Answer

Question 13

Solve the radical equation $$\sqrt{2x - 1} = 5.$$

Accepted Answer

$$x = 13$$

Question 14

Which of the following is the solution to the inequality $$-2x + 5 \u003e 1$$?

Accepted Answer

$$x \u003c 2$$

Question 15

A medical test result is considered normal if it is within 10 units of 100. Which absolute value inequality represents this?

Accepted Answer

$$|x - 100| \leq 10$$

Question 16

Solve the equation $$x^{2/3} = 9$.

Accepted Answer

$$x = 27$$

Question 17

Which of the following best describes the solution set for $$|x + 4| \u003c 7$$?

Accepted Answer

$$-11 \u003c x \u003c 3$$

Question 18

A chemical reaction requires the pH to be no more than 0.5 units away from 7. Which absolute value inequality models this requirement?

Accepted Answer

$$|pH - 7| \leq 0.5$$

Question 19

Solve the quadratic equation $$x^2 + 2x - 8 = 0$ by factoring.

Accepted Answer

$$x = 2 or$$ $$x = -4$$

College Algebra Study Guide: Quadratic, Radical, Rational, and Inequality Equations

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