C. Write the quadratic equations in the form ax? + bx+c = 0 given the following roots
1. (4.-7)
2. (1/3, 4)
3. (-8,-6)
4. (0,9)
5. (2/3, 1/2)
1. (4.-7)
2. (1/3, 4)
3. (-8,-6)
4. (0,9)
5. (2/3, 1/2)
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Answer:
1. (4, -7)
(x + 7)(x - 4) = 0
x² - 4x + 7x - 28 = 0
➡️ x² + 3x - 28 = 0
2. (1/3,4)
(x - 1/3)(x - 4) = 0
x² - 4x - 1/3x + 4/3 = 0
x² - 4×3/1×3x - 1/3x + 4/3 = 0
x² - 12/3x - 1/3x + 4/3 = 0
➡️ x² - 13/3x + 4/3 = 0
3. (-8, -6)
(x + 8)(x + 6) = 0
x² + 6x + 8x + 48 = 0
➡️ x² + 14x + 48 = 0
4. (0, 9)
(x - 0)(x -9)
x² - 9x - 0x + 9 = 0
➡️ x² - 9x + 9 = 0
5. (2/3, 1/2)
(x - 2/3)(x - 1/2) = 0
x² - 1/2x - 2/3x + 1/3 = 0
x² - 1×3/2×3x - 2×2/3×2x + 1/3 = 0
x² - 3/6x - 4/6x + 1/3 = 0
➡️ x² - 7/6x + 1/3 = 0