Solving Quadratic Equations by Extracting the Square Root, Study notes of Mathematics

Download Solving Quadratic Equations by Extracting the Square Root and more Study notes Mathematics in PDF only on Docsity!

Solving Quadratic

Equations by

Extracting the

Square Root

Day 4 - 5 Paul Jorel R. Santos

Objective

Solve quadratic equations by extracting the square root.

Activity 8: Simplify

• 1. 1 6. 36 11.
• 2. 4 7. 49 12.
• 3. 9 8. 64 13.
• 4. 16 9. 81 14.
• 5. 25 10.^100 15.

Square Root Property

If x and c are complex numbers and if 𝑥 2 = 𝑐, then 𝑥 = − 𝑐 or 𝑥 = 𝑐.

Example 2

2 − 9 = 0 𝑥 2 = 9 𝑥 = ± 9 𝑥 = ± 3 𝑥 = 𝟑 𝑥 = −𝟑

Example 3

2 − 48 = 0 3 𝑥 2 = 48 𝑥 2 = 16 𝑥 = ± 16 𝑥 = ± 4

Square Root Property

If x and c are complex numbers and if 𝑥 2 = 𝑐, then 𝑥 = − 𝑐 or 𝑥 = 𝑐.

Activity 8

Direction: Solve for the following quadratic equations.

1. 11 𝑧 2 + 7 = 106 2. (𝑥 − 2 ) 2 = 4

Quiz

Direction: In a ¼ sheet of intermediate paper. Solve for the following quadratic equations.

1. 𝑎 2 − 64 = 0 4. 𝑥 2 + 5 = 14 2. 2 𝑏 2 − 32 = 0 5. 𝑝 2 − 196 = 0 3. 3 𝑥 2 − 27 = 0

Homework

Direction: In your notebook. Solve for the following quadratic equations.

1. 𝟐(𝒙 + 𝟑) 𝟐 = 𝟏𝟖 2.^ 𝟑𝒄 2 − 𝟓 = 𝟐𝟓

2

• 3 = 30 8. 2 𝑏 2
• 5 = 19

9. 4𝑝 2 − 3 = 25 10. 3 𝑦 2 + 2 = 47
10. 5 𝑥 2 − 15 = 60 12. 2 𝑏 2 + 3 = 67
11. 𝑥 2 − 15 = 110 14. 𝑦 2 − 32 = 32
12. 𝑎 2
    • 6 = 48 16. 𝑚 2 − 3 = 22

2

• 3 = 53 22. 7 𝑞 2 − 4 = 10

18. 7 𝑝 2 − 2 = 54 23. 5 𝑘 2 + 3 = 18
19. 5 𝑥 2
    • 1 = 21 24. 54 𝑎 2 − 6 = 24
20. 4 𝑎 2 − 33 = 13 25. 3 𝑐 2 − 5 = 25
21. 2𝑦 2
    • 6 = 15