Jul 6, 2026 杂项（代数） #math f(x)=ax2+bx+c=(x1−m)(x2−m)=x1x2−m(x1+x2)+m2=ca+mba+m2=am2+bm+ca=f(m)a\begin{align} f(x)&=ax^2+bx+c\\ &=(x_{1}-m)(x_{2}-m)\\ &=x_{1}x_{2}-m(x_{1}+x_{2})+m^2\\ &=\frac{c}{a}+\frac{mb}{a}+m^2\\ &=\frac{am^2+bm+c}{a}\\ &=\frac{f(m)}{a}\\ \end{align} f(x)=ax2+bx+c=(x1−m)(x2−m)=x1x2−m(x1+x2)+m2=ac+amb+m2=aam2+bm+c=af(m)
