Question 1

Which of the following equations is NOT a quadratic equation in $$x$$?

Accepted Answer

$$3x = 6$$

Question 2

Solve the equation $$x^2 - 16 = 0$ by factoring. What is the solution set?

Accepted Answer

$$\{-4, 4\}$$

Question 3

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

Accepted Answer

Two distinct complex (non-real) solutions

Question 4

A rectangular garden has a length that is 6 meters more than its width. If the area is 160 square meters, what is the width of the garden?

Accepted Answer

$$10$$ meters

Question 5

Solve the equation $$x^2 + 6x + 13 = 0$ using the quadratic formula. What are the solutions?

Accepted Answer

$$x = -3 \pm 2i$$

Question 6

Which of the following is the standard form of the complex number $$(4 + 3i) - (2 - 5i)$$?

Accepted Answer

$$2 + 8i$$

Question 7

Evaluate $$i^{35}.$$

Accepted Answer

$$-i$$

Question 8

Which of the following is the modulus of the complex number $$z = -3 + 4i$$?

Accepted Answer

$$5$$

Question 9

Solve the radical equation $$\sqrt{x + 3} = x - 1. $$Which of the following is a solution?

Accepted Answer

$$x = 2$$

Question 10

Which of the following statements about the discriminant $$b^2 - 4ac$ is TRUE?

Accepted Answer

If $$b^2 - 4ac$$ \u003c 0$$, the quadratic equation has two complex conjugate solutions.

Question 11

What is the standard form of the product $$(2 + 5i)(3 - 2i)$$?

Accepted Answer

Question 12

Solve the equation $$x^4$$ - $$5x^2 + 4 = 0$. What is the complete solution set?

Accepted Answer

$$\{-2, -1, 1, 2\}$$

Question 13

Which of the following is the reciprocal of $$2 - 3i in $$standard form?

Accepted Answer

$$\frac{2}{13} + \frac{3}{13}i$$

Question 14

A television screen has a width that is 10 inches greater than its height. If the diagonal is 26 inches, what is the height (rounded to two decimal places)?

Accepted Answer

$$15.62$$ inches

Question 15

Solve the equation $$x^3$$ + $$x^2 - x - 1 = 0$ by factoring. What is the solution set?

Accepted Answer

$$\{-1, 1\}$$

Question 16

Which of the following is the correct simplification of $$\sqrt{-18}$$?

Accepted Answer

$$3\sqrt{2}i$$

Question 17

If $$z = 4 - 3i$$, what is the value of $$z \cdot \overline{z}$$?

Accepted Answer

$$25$$

Question 18

Solve the equation $$\sqrt{2x + 3} = x. $$Which of the following is a solution?

Accepted Answer

$$x = 3$$

Question 19

Which of the following is the principal square root of $$-20$$?

Accepted Answer

$$2\sqrt{5}i$$

Quadratic and Radical Equations, Complex Numbers, and Related Techniques

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