Question

Tìm m để các phương trình sau có nghiệm

a) \(\left(m-1\right)x^2-2\left(m+3\right)x-m+2\) = 0

b) \(\left(m-1\right)x^2+2\left(m-3\right)x+m+3=0\)

Answer 1

a/ \(\left[{}\begin{matrix}m=1\\\Delta'=\left(m+3\right)^2-\left(m-1\right)\left(-m+2\right)\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}m=1\\2m^2+3m+11\ge0\end{matrix}\right.\)

\(\Rightarrow\) Pt luôn có nghiệm với mọi m

b/ \(\left[{}\begin{matrix}m=1\\\Delta'=\left(m-3\right)^2-\left(m-1\right)\left(m+3\right)\ge0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}m=1\\-8m+12\ge0\end{matrix}\right.\) \(\Rightarrow m\le\frac{3}{2}\)