How can you show that a generalization is likely correct? (in math)

A generalization is defined as a broad idea, being applied to a group of people or things that are not entirely true.

Because there are always some examples of individuals or situations, where the generalization does not hold true.

For example-

I see two women wearing hats. So I will generalize that all women wear hats. This is wrong.

And when generalization is true in math like. for count by 10 rule, we know that the ones place stays the same and the tens place changes by one number. Like 21,31,41,51 Here we can say that generalization is likely correct.

x² + 3x + 7 = 0       [ax² + bx + c]

a = 1

b = 3

c = 7

quadratic formula:

    (+/- is this ±)

plug in the numbers into the variables

your answer is a