If α and β are the zeroes of the quadratic polynomial f(x) = x2 + x – 2, find the value of 1/α – 1/β.
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x2 + x - 2 = 0
x2 +2x - x - 2 = 0
x(x + 2) -1(x + 2) = 0
(x - 1)(x + 2) = 0
x - 1 = 0 and x + 2 = 0
Hence, x = 1, -2.
Now, let α = 1 and β = -2,
1/α - 1/β
= 1/1 - 1/(-2)
= 1 + 1/2
= 3/2
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