Answer:
Step-by-step explanation:
The catch is to put this into the quadratic and solve for a b and c in three equations.
x = 1
a(1)^2 + b(1) + c= 0
a + b + c + 0 (1)
x = - 1
a(-1)^2 + b(-1) + c = 2
a - b + c = 2 (2)
x = 2
a(2)^2 + b(2) + c = 8
4a + 2b + c = 8 (3)
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Add 1 and 2 together
a + b + c = 0
a - b + c = 2
2a + 2c = 2 Divide by 2
a + c = 1 (4)
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Multiply (2) by 2
2a - 2b + 2c = 4 (5)
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Add (5) + (3)
2a - 2b + 2c = 4
4a + 2b + c = 8
6a + 3c = 12 (6)
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Multiply (4) by 3
3a + 3c = 3 (7)
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Subtract (7) from (6)
6a + 3c = 12
3a + 3c = 3
3a = 9 Divide by 3
3a/3 = 9/3
a = 3
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Use (4) to find c
a + c = 1
3 + c = 1 Subtract 3 from both sides
3-3 + c = 1-3
c = - 2
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Use 1 to find b
3 + b - 2 = 0 Combine 3 and -2
1 + b = 0 Subtract 1 from both sides
b = - 1
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Answers
a = 3
b = - 1
c = - 2
