\(\left\{{}\begin{matrix}F\left(x\right)=3x^2-2x-1\\F\left(x\right)=0\end{matrix}\right.\)\(\Rightarrow3x^2-2x-1=0\)
\(\Rightarrow 3x^2-3x+x-1=0\)
\(\Rightarrow3x\left(x-1\right)+\left(x-1\right)=0\)
\(\Rightarrow\left(3x+1\right)\left(x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}3x+1=0\\x-1=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{3}\\x=1\end{matrix}\right.\)
Xét \(3x^2-2^x-1=0\)
=\(3x^2-3x+x-1=0\)
=\(3x.\left(x-1\right)+\left(x-1\right)\)
=\(\left(3x+1\right).\left(x-1\right)\)
\(\Rightarrow3x+1=0\) hoặc \(x-1=0\)
\(x=\dfrac{-1}{3}\) hoặc \(x=1\)
Vậy \(x\in\left(\dfrac{-1}{3};1\right)\)để\(f\left(x\right)=0\)
