Question

Determine:
m de modo que a função f(x)=3x²-x+m admita, no conunto dos números reais, dois zeros reais;

Answer 1

$\mathsf{Ola\´~Igor,}$

$\mathsf{Para~que~a~func\~ao~admita~2~valores~reais~o~delta~precisa}\\\mathsf{ser~maior~que~0}\\\\\mathsf{f(x)=3x^2-x+m }\\\\\mathsf{\Delta\ \textgreater \ 0}\\\\\mathsf{\Delta=(-1)^2-4.3.m}\\\mathsf{1-12m\ \textgreater \ 0~*(-1)}\\\mathsf{12m-1\ \textless \ 0}\\\\\mathsf{\boxed{m\ \textless \ \frac{1}{12}}}\\\\\\\\\mathsf{\boxed{S=\{x\in~\mathbb{R}~|~m~\ \textless \ \frac{1}{12}\}}}$

$\mathsf{Du\´vidas?~comente}$