A syllogism with of two negative premises has no valid conclusion.
For example Open in Syllogism-Finder App:
No polygon is a circle.
No rectangle is a circle.
Therefore, no rectangle is a polygon.
Negative statements have much less descriptive power than positive ones – we learn less about A from the statement “A is not a tree” than from the statement “A is a house”. Therefore, there are a number of restrictions on what can be done with negative statements.
Even with only a single negative premise, it is no longer possible to draw any positive conclusion (affirmative conclusion from a negative premise).
If both premises are negative, there are no ways in which the middle term can reliably connect the statements. Therefore, it is not possible to infer a conclusion which connects the major and minor terms. In other words: it is not possible to draw a conclusion.