DAY 2: ACTIVITY 2: Solving quadratic equation using factoring method.Factorise these quadratic equations. Positive values only.1. x² + 3x + 2 = 0 x= -2 or -12. a² + 7a + 6 = 03. b² + 4b + 4 = 04. c² - 5c + 6 = 05. d² - 8d + 12 = 06. e² + 6e + 8 = 07. f² + 7f + 10 = 08. g² + 8g + 7 = 09. h² + 10h + 9 = 010. i² + 8i + 16 = 011. j² + 7j + 12 = 012. k² + 10k + 16 = 013. m² + 8m + 15 = 014. n² + 12n + 20 = 015. p² + 9p + 18 = 0
Answer (1)
Answer:Here are the factorizations and positive solutions for each quadratic equation: 2. a² + 7a + 6 = 0Factor: (a + 6)(a + 1) = 0Solutions: a = -6, -1 → Positive value: None3. b² + 4b + 4 = 0Factor: (b + 2)(b + 2) = 0 or (b + 2)² = 0Solution: b = -2 → Positive value: None4. c² - 5c + 6 = 0Factor: (c - 2)(c - 3) = 0Solutions: c = 2, 3 → Positive values: 2, 35. d² - 8d + 12 = 0Factor: (d - 6)(d - 2) = 0Solutions: d = 6, 2 → Positive values: 6, 26. e² + 6e + 8 = 0Factor: (e + 4)(e + 2) = 0Solutions: e = -4, -2 → Positive value: None7. f² + 7f + 10 = 0Factor: (f + 5)(f + 2) = 0Solutions: f = -5, -2 → Positive value: None8. g² + 8g + 7 = 0Factor: (g + 7)(g + 1) = 0Solutions: g = -7, -1 → Positive value: None9. h² + 10h + 9 = 0Factor: (h + 9)(h + 1) = 0Solutions: h = -9, -1 → Positive value: None10. i² + 8i + 16 = 0Factor: (i + 4)(i + 4) = 0 or (i + 4)² = 0Solution: i = -4 → Positive value: None11. j² + 7j + 12 = 0Factor: (j + 4)(j + 3) = 0Solutions: j = -4, -3 → Positive value: None12. k² + 10k + 16 = 0Looking for two numbers that multiply to 16 and add to 10: 8 and 2Factor: (k + 8)(k + 2) = 0Solutions: k = -8, -2 → Positive value: None13. m² + 8m + 15 = 0Factor: (m + 5)(m + 3) = 0Solutions: m = -5, -3 → Positive value: None14. n² + 12n + 20 = 0Looking for two numbers that multiply to 20 and add to 12: 10 and 2Factor: (n + 10)(n + 2) = 0Solutions: n = -10, -2 → Positive value: None15. p² + 9p + 18 = 0Looking for two numbers that multiply to 18 and add to 9: 6 and 3Factor: (p + 6)(p + 3) = 0Solutions: p = -6, -3 → Positive value: None Summary of equations with positive solutions: - Equation 4: c = 2, 3- Equation 5: d = 2, 6 Note: Most quadratics given have negative roots only.
