methods in solving quadratic equations G9 EXTRACTING THE ROOTS.pptx
- 1. “Let all that we do be done in LOVE!”1-Cor. 16-14 ZAMBOANGA CITY DIVISION CULIANAN NATIONAL HGH SCHOOL SOLVING QUADRATIC EQUATION AUGUST 19, 2024 MATH 9
- 3. At the end of the session, the learners are expected to: a. express quadratic equation in the form x2 = k; b. solve quadratic equation by extracting square roots; and c. demonstrate perseverance in doing the activity. OBJECTIVES
- 4. Find the following square roots. REVIEW 6. 7. 8. 9. 10.
- 5. ACTIVITY REAL ROOTS Directions: Solve the following quadratic equations by extracting square roots. Show your solution. 1. 2. 4. 5.
- 6. Guide Questions: 1. How did you solve each equation? 2. What mathematics concepts or principles did you apply to come up with the solution of each equation?
- 7. Quadratic equations that is written in the form x2 =k can be solve by applying the following properties: If k > 0, then x2 =k has two real solutions or roots: x= ± √k. If k = 0, then x2 =k has one real solution or root: x=0. If k < 0, then x2 =k has no real solutions or roots: x= ± √k. The method of solving the quadratic equation x2 =k is called extracting square root.
- 8. To solve an incomplete quadratic equation: Solve the equation for the square of the unknown number. Find the square roots of both members of the equation
- 9. 1. 2. 3. 6. 4. 7. 5. 8. Solve the following quadratic equations by extracting square roots TRY THIS
- 10. QUIZ Directions: Find the solutions of the following quadratic equations by matching column B with column A. write your answer on the box provide to each number. COLUMN A COLUMN B 1. x2 - 1 = 0 a. 0 2. x2 - 195 = 1 b. ±20 3. x2 = 400 c. ±14 4. x2 - 4 = 780 d. No solution x2 -14 = 14 e. ±1 f. 40
- 11. Arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. Provide the general formula for the nth term of an arithmetic sequence: an=a1 + (n−1)d where: an is the nth term a1 is the first term d is the common difference n is the position of the term in the sequence.
- 12. Identifying Missing Terms: Example: Given the sequence 2, 6, __, 14, find the missing term. Solution: Common difference d =6 – 2 = 4, so the missing term is 6+4=10
- 13. Finding the nth Term: Illustrate how to use the formula to find the nth term of a sequence. Example: Find the 10th term of the sequence 3, 7, 11, 15, ... Solution: a1 = 3 d = 4 n = 10 a10 = 3 + (10−1) ×4 a10 = 3 + (9) 4 = 3 + 36 = 39
- 14. Finding the nth Term: Illustrate how to use the formula to find the nth term of a sequence. Example: Find the 10th term of the sequence 3, 7, 11, 15, ... Solution: a1 = 3 d = 4 n = 10 a10 = 3 + (10−1) ×4 a10 = 3 + (9) 4 = 3 + 36 = 39
- 15. A.Find the missing terms and the nth in each arithmetic sequence. a) 26 , 35, ____, 53, … a7 b) 3, ___ , 21, 30 , …a8 c) 3, 9 , ___, 21, …a10 LET’S TRY
- 16. Quiz Directions: Find the nth term of the following: 1)4, 7, 10, 13, … a9 2)15, 7, -1, -9, … a10 3)7,14, 21, 28, …. a12 4)3, 10, 17, 24, … a8
- 17. Answer the given question: 1)For the arithmetic sequence 3, 9, 15, 21...., the common difference is_________. 2) If the first term of an arithmetic sequence is 7 and the common difference is 2. What are the first two terms of the arithmetic sequence? 3) 1.2, 2.2, 3.3, 4.4 is an arithmetic sequence? a) True b) False 4) What is the 9th term of an arithmetic sequence with a1 = 7 and d = 8? a) 71 b) 72 c) 73 d) 74 5) Find the last term of an arithmetic sequence whose a1 = 1, d = 2 and n = 1001. a) 2001 b) 2002 c) 2003 d) 2004