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Question
Given that x + 2 and x + 3 are factors of 2x3 + ax2 + 7x - b. Determine the values of a and b.
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Solution
If x + 2 is a factor is 2x3 + ax2 + 7x - b then x + 2 = 0, x = -2 in equation
2(-2)3 + a (-2)2 + 7(-2) - b = 0
2(-8) + a(4) + 7(-2) - b = 0
-16 + 4a - 14 - b = 0
4a - b = 30 ...(1)
Also given that x + 3 is a factor of
2x3 + ax2 + 7x - b, then x + 3 = 0
x = -3 in equation
2(-3)3 + a(-3)2 + 7(-3) - b = 0
2(-27) + a(9) + 7(-3) - b = 0
-54 + 9a - 21 - b = 0
9a - b = 75 ...(2)
Solving (1) and (2) we get
a = 9, b = 6.
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