Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

2x^{2} + ax – a^{2} = 0

Given: 2x^{2} + ax – a^{2} = 0

Comparing with standard quadratic equation Ax^{2} + Bx + C = 0

A = 2, B = a, C = – a^{2}

Discriminant D = B^{2} – 4AC

= (a)^{2} – 4.2. – a^{2}

= a^{2} + 8 a^{2} = 9a^{2} ≥0

Hence the roots of equation are real.

Roots are given by

Hence the roots of equation are

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