Question

Determine os zeros da função f(t)= x² -3x + 2,e assinale qual das alternativas realizou a leitura correta dos sinais de função. *​

Answer 1

$\sf{f(x)=x^2-3x+2}\\\sf{f(x)=0\implies~x^2-3x+2=0}\\\sf{\Delta=(-3)^2-4\cdot1\cdot2}\\\sf{\Delta=9-8}\\\sf{\Delta=1}\\\sf{x=\dfrac{-b\pm\sqrt{\Delta}}{2a}}\\\sf{x=\dfrac{-(-3)\pm\sqrt{1}}{2\cdot1}}\\\sf{x=\dfrac{3\pm1}{2}}\begin{cases}\sf{x_1=\dfrac{3+1}{2}=\dfrac{4}{2}=2}\\\sf{x_2=\dfrac{1-3}{2}=-\dfrac{2}{2}=-1}\end{cases}$

$\sf{Estudo~do~sinal~da~func_{\!\!\!,}\tilde{a}o:}\\\sf{a=1\textgreater0~concavidade~para~cima}\\\boxed{\sf{f(x)\textgreater0\implies~x\textless1~~ou~~x\textgreater2}}\\\boxed{\sf{f(x)\textless0\implies~1\textless~x~\textless2}}$