What is the value of a for which ax^2 + a^2x + a^3 = 0 has real roots.

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The roots of a quadratic equation ax^2 + bx + c = 0 are real if `b^2 - 4ac >= 0`

The roots of the equation ax^2 + a^2x + a^3 = 0 are real if `(a^2)^2 - 4*a*a^3 >= 0`

=> `a^4 - 4a^4 >= 0`

=> `a^4 >= 4a^4`

a^4 is a positive number and so is 4. This makes `4a^4 > a^4` for all values of a.

For no value of a does the given equation have real roots.

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