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Question
Solve the following quadratic equations by factorization:
x2 - x - a(a + 1) = 0
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Solution
We have been given
x2 - x - a(a + 1) = 0
x2 + ax - (a + 1)x - a(a + 1) = 0
x(x + a) - (a + 1)(x + a) = 0
(x - (a + 1))(x + a) = 0
Therefore,
x - (a + 1) = 0
x = (a + 1)
or,
x + a = 0
x = -a
Hence, x = a + 1 or x = -a
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