WAEC - Mathematics (2013 - No. 29)
Given that P = x2 + 4x - 2, Q = 2x - 1 and Q - p = 2, find x
-2
-1
1
2
Explanation
P = x2 + 4x - 2, Q = 2x - 1
Q - p = 2, (2x - 1) - (x2 + 4x - 2) = 2
2x - 1 - x2 - 4x + 2 = 2
-2x - x2 + 1
-x2 - 2x - 1 = 0
x2 + 2x + 1 = 0
x2 + x + x + 1 = 0
x(x + 1) + 1(x + 1) = 0
(x + 1)(x + 1) = 0
x + 1 = 0 or x + 1 = 0
x = -1 or x = -1
x = -1
Q - p = 2, (2x - 1) - (x2 + 4x - 2) = 2
2x - 1 - x2 - 4x + 2 = 2
-2x - x2 + 1
-x2 - 2x - 1 = 0
x2 + 2x + 1 = 0
x2 + x + x + 1 = 0
x(x + 1) + 1(x + 1) = 0
(x + 1)(x + 1) = 0
x + 1 = 0 or x + 1 = 0
x = -1 or x = -1
x = -1
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