Math 0314/1314 Unit 4 Review

Flashcards to review key concepts and problem-solving techniques in algebra, including simplifications, quadratic equations, and inequalities.

What is the result of simplifying −√1?

−1

What is the simplification of √(−12)²?

12

What does √c² equal?

|c|

What is the simplification of √(4x − 3)²?

|4x − 3|

What is the value of (√19.2)²?

19.2

What is the simplification of −√−49?

−7i

What is the result of √−169?

13i

What is the simplified form of 3 − √−25?

3 − 5i

What is the value of √x⁵?

x^(5/2)

What is the simplification of √25 − 9?

4

What does 5√64 simplify to?

40

What is the value of √(−13)² − (4)(−3)(−4)?

11

What is the simplification of √−125/3?

−5i√5/3

What is 2 + √−16/2?

1 + 2i

What is the simplification of √80?

4√5

What does √54 simplify to?

3√6

What is the simplification of √48/3?

2√6

What does √121 equal?

11

What is √18/3?

3√2

What is √250/3?

5√2/3

What are the roots of 2x² + 15x = 8?

x = −8, x = 1/2

What are the roots of 5x² + 20x = 0?

x = −4, x = 0.

Using the square root method, solve 2x² − 3 = 125.

x = ±8.

What is the solution to x²/2 + 5 = −3?

x = ±4i.

What are the roots of the equation (x + 3)² = −10?

x = −3 ± i√10.

What are the solutions of (3x − 4)² = 18?

x = 4 ± 3√2/3.

How do you solve x² − 12x + 27 = 0?

x = 3, x = 9.

What does the quadratic formula yield for x² − 2x + 19 = 0?

x = 1 ± 3i√2.

What does doing synthetic division of (3x⁴ + 11x³ − 20x² + 7x + 35) ÷ (x + 5) yield?

3x³ − 4x² + 7.

According to the Rational Zero Theorem, what are the possible rational zeros for f(x) = 3x⁵ − 2x⁴ − 15x³ + 10x² + 12x − 8?

±(1, 2, 4, 8, 1/3, 2/3, 4/3, 8/3).

What are the zeros of f(x) = x³ + 3x² − 4?

x = −2, x = 1.

What are the values for the roots of f(x) = 6x³ + x² − 4x + 1?

x = −1, x = 1/3, 1/2.

What is the solution set for 2x² + 5x − 3 < 0? (Express in interval notation)

(−3, 1/2).

What are the solution intervals for 2x² + 9x + 4 ≥ 0?

(−∞, −4] ∪ [−1/2, ∞).

What is the graphical solution for x³ + 2x² > 3x?

(−3,0) ∪ (1, ∞).

What are the solutions for (x + 1)(x − 2)/(x − 1) ≥ 0? (Express in interval notation)

[−1, 1) ∪ (2, ∞).