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Answer (1)
Answer:Here are the solutions for the given quadratic equations: 1. 5x² + 17x + 6 = 0 This quadratic equation can be solved by factoring. We look for two numbers that add up to 17 and multiply to 30 (5 x 6). These numbers are 15 and 2. Therefore, we can rewrite the equation as: (5x + 2)(x + 3) = 0 Solving for x, we get: 5x + 2 = 0 => x = -2/5 or -0.4 x + 3 = 0 => x = -3 Therefore, x = -2/5 or x = -3 2. 4x² - 9x - 10 = 0 This equation can also be solved by factoring. We need two numbers that add up to -9 and multiply to -40 (4 x -10). These numbers are -16 and 5. We can rewrite the equation as: (4x +5)(x -2) = 0 Solving for x: 4x + 5 = 0 => x = -5/4 or -1.25 x - 2 = 0 => x = 2 Therefore, x = -5/4 or x = 2 3. 15x² + 29x - 14 = 0 This equation is best solved using the quadratic formula: x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} Where a = 15, b = 29, and c = -14. Substituting these values: x = \frac{-29 \pm \sqrt{29^2 - 4(15)(-14)}}{2(15)} x = \frac{-29 \pm \sqrt{841 + 840}}{30} x = \frac{-29 \pm \sqrt{1681}}{30} x = \frac{-29 \pm 41}{30} This gives us two solutions: x = (-29 + 41) / 30 = 12/30 = 2/5 or 0.4 x = (-29 - 41) / 30 = -70/30 = -7/3 or approximately -2.33 Therefore, x = 2/5 or x = -7/3Step-by-step explanation:Hope it's help, good luck!
