1. For all real numbers $x$, the values of all quadratic functions $f(x)=a x^{2}+b x+c(a<b)$ are always non-negative real numbers, $M=\frac{a+b+c}{b-a}$ has the minimum value of $\qquad$ .
1. 3 .
$a>0, b^{2}-4 a c \leqslant 0$, i.e., $c \geqslant \frac{b^{2}}{4 a}$. Let $b-a=t(t>0)$, then $M \geqslant \frac{a+(t+a)+\frac{(a+t)^{2}}{4 a}}{t}=$ $\frac{(3 a+t)^{2}}{4 a t} \geqslant \frac{(2 \sqrt{3 a t})^{2}}{4 a t}=3$. The equality holds if and only if $3 a=t, c=\frac{b^{2}}{4 a}$, i.e., $b=c=4 a$, thus $M_{\text {min }}=3$