MathDB

Replacing any of the coefficients of quadratic trinomial

f(x)=ax^2+bx+c

with an

1

will result in a quadratic trinomial with at least one real root. Prove that the resulting trinomial attains a negative value at at least one point.
EDIT: Oops I failed, added "with a 1." Also, I am sorry for not knowing these are posted already, however, these weren't posted in the contest lab yet, which made me think they weren't translated yet.
Note: fresh translation

Problem Statement