Question

Vă rog, urgent!!! Nivel liceu mate-info intensiv ​

Answer 1

$f(x) = x^2+mx+m+1 = 0\\ \\ x_1<1<x_2 \Big|-1 \\ \\ x_1-1<0<x_2-1 \Big|:(x_2-1), \quad \{x_2-1>0\}\\ \dfrac{x_1-1}{x_2-1} < 0 <1 \\ \\ \dfrac{x_1-1}{x_2-1}<0\Big|\cdot (x_2-1)^2 \\ \\ (x_1-1)(x_2-1) < 0 \\ \\ f(x) = (x-x_1)(x-x_2) = (x_1-x)(x_2-x) \\ \\f(1) = (x_1-1)(x_2-1)\\ \\ f(1) < 0 \\ \\ 1^2+m+m+1 < 0 \Rightarrow 2m+2<0 \Rightarrow 2m<-2 \Rightarrow m<-1 \Rightarrow\\ \\ \Rightarrow \boxed{m\in (-\infty, -1)} \Rightarrow \text{a) corect}$