f(x) ≤ 0 ∀ x∈ \([0;1]\) ⇔ \(\left\{{}\begin{matrix}\Delta'>0\\\left(x_1-1\right)\left(x_2-1\right)\ge0\\x_1+x_2\ge2\end{matrix}\right.\)
⇔\(\left\{{}\begin{matrix}m^2-3m+3>0\\-m+1\ge0\\2m-2\ge2\end{matrix}\right.\)
⇔\(\left\{{}\begin{matrix}\forall m\\m\le1\\m\ge2\end{matrix}\right.\)
⇔∅. Vậy không có giá trị m thỏa mãn