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.
🙂 🙂 🙂
Nalin Pithwa