Question

F(x)= -3x^2 +6x +3m

Tìm m để f(x) <=0 với mọi x thuộc khoảng (-oo; -1)

Giải hộ mình với, please

Answer 1

TH1: \(\Delta'=9+9m\le0\Rightarrow m\le-1\)

TH2: \(\left\{{}\begin{matrix}\Delta'>0\\-1\le x_1< x_2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}m>-1\\\left(x_1+1\right)\left(x_2+1\right)\ge0\\\frac{x_1+x_2}{2}>-1\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}m>-1\\x_1x_2+x_1+x_2+1\ge0\\x_1+x_2>-2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}m>-1\\-m+2+1\ge0\\2>-1\end{matrix}\right.\) \(\Rightarrow-1< m\le3\)

Vậy \(m\le3\)