What do you mean by "replacing"? Like shuffling them, e.g. $ax^2+bx+c \rightarrow cx^2+ax+b$? Also, I'm assuming that $a,b,c \in \mathbb{R}$?

Based on the original problem statement here, I believe the translation should be: The quadratic function $f(x)=ax^2+bx+c$ with real coefficients has the property that if we replace any one of its coefficients with a $1$, then the resulting quadratic function has at least one real root. Prove that for the original function $f$, there is some real number $x$ for which $f(x)$ is negative. In other words, $f(x)=ax^2+bx+c$ is a quadratic function with real coefficients such that each of the functions \[ f_1(x)=1x^2+bx+c,\qquad f_2(x)=ax^2+1x+c,\qquad f_3(x)=ax^2+bx+1\] has at least one real root. Prove the $f(x)$ is negative for some real number $x$.