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

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