Question 1

Which of the following is the correct standard form of a quadratic equation?

Accepted Answer

$$ax^2 + bx + c = 0$

Question 2

Solve the equation $$3(2 - 5x) = 4x + 25$$ for $$x.$$

Accepted Answer

$$x = rac{1}{2}$$

Question 3

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

Accepted Answer

If $$b^2 - 4ac$$ \u003e 0$$, there are two distinct real solutions.

Question 4

Simplify $$\sqrt{-75}.$$

Accepted Answer

$$5i\sqrt{3}$$

Question 5

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

Accepted Answer

$$13$$

Question 6

Which of the following is the conjugate of $$4 - 5i$$?

Accepted Answer

$$4 + 5i$$

Question 7

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

Accepted Answer

$$x = -3, x = 2$$

Question 8

Which of the following is the correct solution to $$i^{85}$$?

Accepted Answer

$$i$$

Question 9

Express the set $$\{x | 0 \u003c x \u003c 5\} in $$interval notation.

Accepted Answer

$$(0, 5)$$

Question 10

Solve the inequality $$2x + 12 \u003e 19$$ and express the solution in interval notation.

Accepted Answer

$$(3.5, \infty)$$

Question 11

Which of the following is the best method to solve $$(x + 2)^2$ = 9$$?

Accepted Answer

Square root property

Question 12

Solve the quadratic equation $$2x^2 + 7x + 6 = 0$ by factoring.

Accepted Answer

$$x = -2, x = -1.5$$

Question 13

Which of the following is the standard form of the complex number $$4 + 3i$$?

Accepted Answer

$$4 + 3i$$

Question 14

What is the solution set for the equation $$x = x + 4$$?

Accepted Answer

No solution (inconsistent)

Question 15

Which of the following is the correct result of dividing $$6 + i by$$ $$4 - 2i$$? Express your answer in standard form.

Accepted Answer

$$\frac{22}{20} + \frac{16}{20}i$$

Question 16

Which of the following is the correct solution to $$x^2 + 6x + 1 = 0$ using the quadratic formula?

Accepted Answer

$$x = -3 \pm 2\sqrt{2}$$

Question 17

Which of the following is the correct interval notation for the set $$\{x | x \geq 3\}$$?

Accepted Answer

$$[3, \infty)$$

Question 18

If $$i = \sqrt{-1}$$, what is $$i^{100}$$?

Accepted Answer

$$1$$

Question 19

Which of the following is the correct solution to $$x^2 = -4$?

Accepted Answer

$$x = 2i, x = -2i$$

Question 20

Which of the following is the correct solution to the rational equation $$\frac{x}{x-1} = 7$$?

Accepted Answer

$$x = \frac{7}{6} is $$not correct; the correct answer is $$x = \frac{7}{6}$$, but $$x 
eq 1 is $$the restriction.

Linear and Quadratic Functions: Solving Equations, Complex Numbers, and Inequalities

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