Question

Tìm m để f(x)=\(x^2-2\left(m-1\right)x+m-2\le0\forall x\in\left[0;1\right]\)

Answer 1

Ta có : \(\left\{{}\begin{matrix}a=1>0\\\Delta'=\left(m-1\right)^2-\left(m-2\right)=m^2-3m+3>0\end{matrix}\right.\)

Để \(f\left(x\right)\le0\forall x\in\left[0;1\right]\)

\(\Leftrightarrow x_1\le0< 1\le x_2\)

\(\Rightarrow\left\{{}\begin{matrix}f\left(0\right)\le0\\f\left(1\right)\le0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}m-2\le0\\-m+1\le0\end{matrix}\right.\Rightarrow1\le m\le2\)

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