1.ײ+6×+9=0 2.ײ+5×+10=0 3.2ײ-9×-5=04.2ײ-10×+8=0
Answer (1)
Answer:Let's solve each quadratic equation step by step.---1. x² + 6x + 9 = 0Factor the trinomial:> x² + 6x + 9 = (x + 3)(x + 3) = (x + 3)²So,x + 3 = 0x = -3✅ Solution: x = -3 (multiplicity 2)---2. x² + 5x + 10 = 0Use the quadratic formula:> x = [-b ± √(b² - 4ac)] / 2aHere, a = 1, b = 5, c = 10> x = [-5 ± √(25 - 40)] / 2x = [-5 ± √(-15)] / 2x = [-5 ± i√15] / 2✅ Solution: x = (-5 ± i√15) / 2 (complex roots)---3. 2x² - 9x - 5 = 0Use the quadratic formula:a = 2, b = -9, c = -5> x = [9 ± √(81 + 40)] / 4x = [9 ± √121] / 4x = [9 ± 11] / 4So:x = (9 + 11)/4 = 20/4 = 5x = (9 - 11)/4 = -2/4 = -0.5✅ Solution: x = 5 and x = -0.5---4. 2x² - 10x + 8 = 0Divide the entire equation by 2:> x² - 5x + 4 = 0Factor:> (x - 4)(x - 1) = 0✅ Solution: x = 4 and x = 1---✅ Final Answers:1. x² + 6x + 9 = 0 → x = -32. x² + 5x + 10 = 0 → x = (-5 ± i√15) / 23. 2x² - 9x - 5 = 0 → x = 5, x = -0.54. 2x² - 10x + 8 = 0 → x = 4, x = 1
