Question

f (x) = mx² - 2(m-1)x + 4m. Tìm m để f(x) luôn nhận giá trị âm

Answer 1

\(f\left(x\right)< 0\forall x\in R.\\ \Leftrightarrow\left\{{}\begin{matrix}m< 0.\\\Delta'=m^2-2m+1-4m^2< 0.\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}m< 0.\\\Delta'=-3m^2-2m+1< 0.\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}m< 0.\\\left[{}\begin{matrix}m< -1.\\m>\dfrac{1}{3}.\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow m< -1.\\ \Leftrightarrow m\in\left(-\infty;-1\right).\)