1. (2 points) Among six different quadratic trinomials that differ by the permutation of coefficients, what is the maximum number that can have two distinct roots
Answer: 6

Solution: Let's take, for example, the coefficients, $-5,1,2$.

If the number -5 is the leading coefficient or the constant term, the equation obviously has two roots of different signs.

For the case when -5 is the second coefficient, let's calculate the discriminant: $5^{2}-1 \cdot 2=23>0$.