x^{2} + 6x – (a^{2} + 2a – 8) = 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

=

And either of their sum or difference = b

=

Thus the two terms are (a + 4) & (a-2)

Difference = (a + 4)-(a-2)

= 6

Product = (a + 4)(a-2)

=

x[x + (a + 4)]-(a-2)[x + (a + 4)] = 0

[x-(a-2)][x + (a + 4)] = 0

[x-(a-2)] = 0 or [x + (a + 4)] = 0

x = (a-2) or x = -(a + 4)

Hence roots of equation are x = (a-2) or-(a + 4)

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