Solve each of the following quadratic equations:

2x^{2} + ax - a^{2} = 0

Using the 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 = 2; b = a; c = - a^{2}

= - 2.a^{2} = - 2 a^{2}

And either of their sum or difference = b

= a

Thus the two terms are 2a and - a

Difference = 2a - a = a

Product = 2a. - a = - 2a^{2}

2x (x + a)-a (x + a) = 0

(2x-a) (x + a) = 0

(2x-a) = 0 or (x + a) = 0

Hence the roots of equation are

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