1. Which of the following represents a quadratic equation?
A. 2 − 6 + 7
B. 22 + 2 + 7 = 0
C. 32 − 6 = 10
D. 2−2 + 8 + 15 = 0

2. What is the most appropriate method to solve the quadratic equation 2 − 16 = 0?
A. By extracting the square root
B. By factoring
C. By completing the square
D. By using the quadratic formula

3. Find the roots of the quadratic equation 2 − − 12 = 0.
A. -4 and 4
B. -4 and 3
C. 4 and -3
D. -3 and 3

4. Which quadratic equation has the roots of -5 and 3?
A. 2 + 2 − 15 = 0
B. 2 − 2 − 15 = 0
C. 2 + 2 + 15 = 0
D. 2 − 2 + 15 = 0

5. What are the roots of the quadratic equation 2 − 4 + 1 = 0?
A. 2 + √3 and 2 − √3
B. 2 + √5 and 2 − √5
C. 1 + √3 and 1 − √3
D. 1 + √5 and 1 − √5

6. Which of the following quadratic equations has no real roots?
A. 2– 7 + 12 = 0
B. 22 − 4 – 3 = 0
C. 32 + 4 + 1 = 0
D. 2 – 2 + 5 = 0

7. What is the nature of the roots if the discriminant is positive integer and perfect square?
A. two distinct rational roots
B. two distinct irrational roots
C. two equal rational roots
D. two distinct not real roots

8. What is the sum of the roots of 2– 10 + 1 = 0?
A. -2
B. 10
C. -10
D. 5

9. Find the product of the roots of 42 + 12 + 20 = 0.
A. 4
B. 5
C. 6
D. 12

10. Find the equation whose roots are 4 and –5.
A. 2 − 9 − 20 = 0
B. 2 − − 20 = 0
C. 2 + − 20 = 0
D. 2 + 9 − 20 = 0

11. The sum of two numbers is 12 and the product is 35. What are the numbers?
A. 5 and 7
B. 4 and 8
C. 3 and 9
D. 2 and 10

12. The product of two consecutive positive integers is 56. What are the integers?
A. 6 and 6
B. 6 and 7
C. 7 and 8
D. 8 and 9

13. The length of a garden is 4 meters longer than its width and the area is 45 square meters. How wide is the garden?

A. 4 m
B. 5 m
C. 6 m
D. 9 m

14. The sum of the number and its reciprocal is 10 3 . Find the numbers.
A. 6 and 1 6
B. 5 and 1 5
C. 4 and 1 4
D. 3 and 1 3

15. The ages of three family children can be expressed as consecutive integers. The square of the age of the youngest child is 4 more than eight times the age of the oldest child. Find the age of the oldest child.
A. 6-year-old
B. 11-year-old
C. 10-year-old
D. 12-year-old

16. What inequality contains second-degree polynomial written in any of the following forms 2 + + > 0, 2 + + < 0, 2 + + ≤ 0, or 2 + + ≥ 0?
A. Linear Equation
B. Quadratic Equation
C. Linear Inequality
D. Quadratic Inequality

17. Which of the following is equivalent to 2 + 3 − 10 < 0?
A. ( − 2)( + 5) > 0
B. ( + 2)( + 5) < 0
C. ( − 2)( + 5) < 0
D. ( − 2)( + 5) ≥ 0

18. Find the solution set in interval notation of the inequality 2 − 2 − 15 ≥ 0.
A. [−3, 5]
B. [−5, 3]
C. (−∞, −3] ∪ [5, +∞)
D. (−∞, −5] ∪ [3, +∞)

19. What the solution set in interval notation of the inequality 2 + 4 − 45 < 0? A. (−9, 5) B. (−5, 9) C. (−∞, −9) ∪ (5, +∞) D. (−∞, −5) ∪ (9, +∞) 20. The length of a rectangular garden is 3 m more than the width. How long is the width be to ensure the area is at least 180 2?
A. width is at least 12 m
B. width is at least 13 m
C. width is at least 14 m
D. width is at least 15 m​