Question

Tìm các giá trị của m để biểu thức sau luôn dương :

a) \(x^2-4x+m-5\)

b) \((3m+1)x^2-\left(3m+1\right)x+m+4\)

Answer 1

a/ \(\Delta'=4-\left(m-5\right)< 0\)

\(\Leftrightarrow m>9\)

b/ \(\left\{{}\begin{matrix}3m+1>0\\\Delta=\left(3m+1\right)^2-4\left(3m+1\right)\left(m+4\right)< 0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}m>-\frac{1}{3}\\\left(3m+1\right)\left(-m-15\right)< 0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}m>-\frac{1}{3}\\\left[{}\begin{matrix}m< -15\\m>-\frac{1}{3}\end{matrix}\right.\end{matrix}\right.\) \(\Rightarrow m>-\frac{1}{3}\)