**Question:**

Find the necessary and sufficient condition that the quadratic equation where has one root which is the square of the other.

**Solution:**

Let the two roots of the given quadratic equation , with be and such that .

Then, we know and so that and . From the latter relation, we get that . Substituting this in the first relation of sum of roots, we get the following necessary and sufficient condition:

.

The above is the desired solution.

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Nalin Pithwa

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