Question 1

Which of the following is the correct quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 2

Given the quadratic equation $$x^2 - 4x + 13 = 0$, what type of solutions does it have?

Accepted Answer

Two complex solutions

Question 3

If the discriminant $$D = b^2$ - 4ac of a $$quadratic equation is zero, what can you conclude about its solutions?

Accepted Answer

There is one real solution (a repeated root)

Question 4

Which of the following is the correct factorization of $$x^2 - 36$?

Accepted Answer

$$(x - 6)(x + 6)$$

Question 5

What is the sum and product of the roots of the quadratic equation $$x^2 + 5x + 6 = 0$?

Accepted Answer

Sum: $$-5$$, Product: $$6$$

Question 6

Which of the following expressions is the correct factorization of $$a^2$$ - $$b^2$$?

Accepted Answer

$$(a - b)(a + b)$$

Question 7

Given $$z = 3 + 4i$$, what is the conjugate $$\overline{z}$$?

Accepted Answer

$$3 - 4i$$

Question 8

What is the result of multiplying $$(2 + 3i)$$ and $$(2 - 3i)$$?

Accepted Answer

$$13$$

Question 9

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 10

If $$x^2 + 10x + 18 = 0$, what are the roots?

Accepted Answer

$$x = -5 \pm \sqrt{7}$$

Question 11

Which of the following is a correct statement about the sum of perfect squares?

Accepted Answer

A sum of perfect squares cannot be factored over the real numbers.

Question 12

What is the result of dividing $$1 + i by$$ $$3 - 2i$$?

Accepted Answer

$$\frac{1}{13} + \frac{5}{13}i$$

Question 13

Which of the following is the correct factorization of $$6x^2 + 7x + 10$?

Accepted Answer

Cannot be factored over the real numbers

Question 14

If $$x^2 + 4x + 13 = 0$, what are the solutions?

Accepted Answer

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

Question 15

Which of the following is the correct factorization of $$x^2 + 6x + 9$?

Accepted Answer

$$(x + 3)^2$

Question 16

What is the product of $$(1 + 2i)$$ and $$(3 - i)$$?

Accepted Answer

$$5 + 5i$$

Question 17

Which of the following is the correct factorization of $$x^2 - 2x - 15$?

Accepted Answer

$$(x - 5)(x + 3)$$

Question 18

If $$x^2 + 2x + 5 = 0$, what are the roots?

Accepted Answer

$$x = -1 \pm 2i$$

Question 19

Which of the following is the correct factorization of $$x^3 + 8$?

Accepted Answer

$$(x + 2)(x^2$ - 2x + 4)$$

Polynomials, Quadratic Equations, and Complex Numbers: Precalculus Study Guide

Study Guide - Practice Questions