Question

xét dấu các biểu thức sau

a. f(X)=11X+3/-x²+5x-7

 

Answer 1

\(f\left(x\right)=\dfrac{11x+3}{-x^2+5x-7}.\)

Ta có: \(-x^2+5x-7\) là 1 tam thức bậc 2.

\(\left\{{}\begin{matrix}a=-1< 0.\\\Delta=5^2-4.\left(-1\right).\left(-7\right)=-3< 0.\end{matrix}\right.\)

\(\Rightarrow-x^2+5x-7>0\forall x\in R.\)

\(\Rightarrow\) \(f\left(x\right)>0.\Leftrightarrow11x+3>0.\Leftrightarrow x>\dfrac{-3}{11}.\\ f\left(x\right)< 0.\Leftrightarrow11x+3>0.\Leftrightarrow x>\dfrac{-3}{11}.\\ f\left(x\right)=0.\Leftrightarrow x=\dfrac{-3}{11}.\)