Solve: x^{2} + 5x – (a^{2} + a – 6) = 0

Using splitting middle term, the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation a = 1 b = 5 c =

=

And either of their sum or difference = b

=

Thus the two terms are

Difference =

=

Product =

=

x[x + (a + 3)] - (a - 2)[x + (a + 3)] = 0

[x - (a - 2)][x + (a + 3)] = 0

[x - (a - 2)] = 0 or [x + (a + 3)] = 0

x = (a - 2) or x = - (a + 3)

Hence roots of equation are x = (a - 2)or - (a + 3)

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