Để pt vô nghiệm
a/ \(\left\{{}\begin{matrix}m-4\ne0\\\Delta'=\left(2m-7\right)^2-\left(m-4\right)\left(5m-16\right)< 0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m\ne4\\-m^2+8x-15< 0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}m< 3\\m>5\end{matrix}\right.\)
b/ \(\Delta'=\left(m-1\right)-4\left(m-1\right)< 0\)
\(\Leftrightarrow\left(m-1\right)\left(m-5\right)< 0\)
\(\Rightarrow1< m< 5\)
c/ \(\left\{{}\begin{matrix}2m-3\ne0\\\Delta'=\left(m-3\right)^2-\left(2m-3\right)\left(m-1\right)< 0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m\ne\frac{3}{2}\\-m^2-m+6< 0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}m>2\\m< -3\end{matrix}\right.\)
d/
\(\left\{{}\begin{matrix}m\ne0\\\Delta'=\left(m-1\right)^2-m\left(m-3\right)< 0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}m\ne0\\m+1< 0\end{matrix}\right.\)
\(\Rightarrow m< -1\)
e/
\(\Delta=\left(m+1\right)^2-4\left(m-1\right)< 0\)
\(\Leftrightarrow m^2-2m+5< 0\)
\(\Leftrightarrow\left(m-1\right)^2+4< 0\)
Không tồn tại m thỏa mãn
f/
\(m=1\) pt vô nghiệm (thỏa mãn)
Với \(m\ne1\)
\(\Delta'=\left(m-1\right)^2+\left(m-1\right)< 0\)
\(\Leftrightarrow m\left(m-1\right)< 0\Rightarrow0< m< 1\)
Vậy \(0< m\le1\)
