8. (4 points) On the board, all three-digit natural numbers are written, the first digits of which are odd and greater than 1. What is the maximum number of quadratic equations of the form $a x^{2}+b x+c=0$ that can be formed using these numbers as $a, b$ and $c$, each no more than once, such that all these equations have roots.

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# Answer: 100

## Solution:

In each equation, there must be a coefficient less than five hundred. Otherwise, the discriminant $b^{2}-4 a c$ 2 variant