Question

Solve the following quadratic equations by factorization:

x² - x - a(a + 1) = 0

Answer 1

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