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Tut
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#1
Report Thread starter 15 years ago
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Given that (x - 1) and (x + 1) are factors of px^3 + qx^2 - 3x - 7 find the value of P and Q

Any help very much appreciated
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Christophicus
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Report 15 years ago
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(Original post by Tut)
Given that (x - 1) and (x + 1) are factors of px^3 + qx^2 - 3x - 7 find the value of P and Q

Any help very much appreciated
If (x-1) and (x+1) are factors, f(1) and f(-1) are equal to zero.

f(1) = p + q - 3 - 7 = 0
f(-1) = -p + q + 3 - 7 = 0

q + p = 10
q - p = 4

Add the two equations.
2q = 14
q = 7

q + p = 10
=> p = 10 - q = 10 - 7 = 3

q = 7, p = 3
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Gaz031
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(Original post by Tut)
Given that (x - 1) and (x + 1) are factors of px^3 + qx^2 - 3x - 7 find the value of P and Q

Any help very much appreciated
Alternatively:

(x-1) and (x+1) are factors. Hence (x-1)(x+1) = x^2 - 1 is a factor.

You then need to divide px^3 + qx^2 - 3x - 7 by x^2 - 1. You know there is no remainder so you can use this fact when subtracting the rows to find values of p and q.
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nas7232
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Report 15 years ago
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Given that (x - 1) and (x + 1) are factors of px^3 + qx^2 - 3x - 7 find the value of P and Q

F(1) = p + q - 3 - 7 = 0
F(-1) = -p + q + 3 - 7 = 0

p + q = 10
-p + q = 4

Solving simultaneously

2q = 14
q=7

p + q = 10
p + (7) = 10
Therfore, p = 3
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