Question 1

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

Accepted Answer

$ax^2 + bx + c = 0$

Question 2

A quadratic equation $x^2 + 6x + 9 = 0$ is solved by factoring. What are its solutions?

Accepted Answer

$x = -3$

Question 3

Which property allows you to set each factor equal to zero when solving $ax^2 + bx + c = 0$ by factoring?

Accepted Answer

Zero-Factor Property

Question 4

What is the solution to the equation $4(x-3)^2 = 16$ by extracting square roots?

Accepted Answer

$x = 3 \pm 2$

Question 5

Which step is necessary before factoring the equation $(x-5)(x+2) = 8$?

Accepted Answer

Expand the left side and subtract 8 from both sides

Question 6

What is the solution to $x^2 = 25$ using the method of extracting square roots?

Accepted Answer

$x = \pm 5$

Question 7

When completing the square for $x^2 + 8x = 20$, what number should be added to both sides?

Accepted Answer

$16$

Question 8

Which formula is used to solve any quadratic equation $ax^2 + bx + c = 0$?

Accepted Answer

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

Question 9

For the quadratic equation $x^2 + 4x + 5 = 0$, what is the discriminant and how many real solutions does it have?

Accepted Answer

Discriminant is $-4$; no real solutions

Question 10

A room has an area of $144$ square feet. What is the length of each side if the room is square?

Accepted Answer

$12$ feet

Question 11

The imaginary unit $i$ is defined as:

Accepted Answer

$i = \sqrt{-1}$

Question 12

What is the standard form of the complex number $-5 + 3i$?

Accepted Answer

$-5 + 3i$

Question 13

If $a + bi = c + di$, what must be true?

Accepted Answer

$a = c$ and $b = d$

Question 14

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

Accepted Answer

$5 + 12i$

Question 15

What is the additive inverse of the complex number $a + bi$?

Accepted Answer

$-a - bi$

Question 16

What is the product of the complex conjugates $(a + bi)(a - bi)$?

Accepted Answer

$a^2 + b^2$

Question 17

What is the principal square root of $-9$?

Accepted Answer

$3i$

Question 18

A sunroom is 3 feet longer than it is wide and has an area of $154$ square feet. What are the dimensions of the room?

Accepted Answer

Width $= 11$ ft, Length $= 14$ ft

Question 19

Which of the following best describes the set of complex numbers?

Accepted Answer

All numbers of the form $a + bi$ where $a$ and $b$ are real numbers

Question 20

If the discriminant $b^2 - 4ac$ of a quadratic equation is zero, what does this indicate about the solutions?

Accepted Answer

There is one repeated real solution

Quadratic Equations and Applications: College Algebra Study Notes

Study Guide - Practice Questions