\(\Leftrightarrow\left(\left|x\right|\right)^2-4\left|x\right|-2k+3=0\)
Để phương trình có 4 nghiệm phân biệt thì \(\left\{{}\begin{matrix}\left(-4\right)^2-4\cdot1\cdot\left(-2k+3\right)>0\\\dfrac{4}{1}>0\\\dfrac{-2k+3}{1}>0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}16+8k-12>0\\-2k+3>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}k>-\dfrac{1}{2}\\k< \dfrac{3}{2}\end{matrix}\right.\)