Lời giải:

a.

$|x|\leq 2\Leftrightarrow -2\leq x\leq 2$

Tập $A=[-2;2]$

$(x-1)(x-4)< 0\Leftrightarrow 1< x< 4$

Tập $B=(1;4)$

Đến đây bạn có thể dễ dàng biểu diễn nó trên trục số

b.

$A\cap B=[-2;2]\cap (1;4)=(1;2]$

$A\cup B=[-2;2]\cup (1;4)=[-2;4)$

$A\setminus B= [-2;2]\setminus (1;4)=[-2;1]$

Xét pt hoành độ gđ của đường thẳng và parabol có:

\(\left(m-1\right)x^2+3mx+2m=2x-1\)

\(\Leftrightarrow\left(m-1\right)x^2+x\left(3m-2\right)+2m+1=0\) (1)

Để đt và parabol cắt tại hai điểm pb có hoành độ âm

\(\Leftrightarrow\) Pt (1) có hai nghiệm âm phân biệt

\(\Leftrightarrow\left\{{}\begin{matrix}\Delta>0\\S< 0\\P>0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}m^2-8m+8>0\\\dfrac{2-3m}{m-1}< 0\\\dfrac{2m+1}{m-1}>0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}m\in\left(-\infty;4-2\sqrt{2}\right)\cup\left(4+2\sqrt{2};+\infty\right)\\m\in\left(-\infty;\dfrac{2}{3}\right)\cup\left(1;+\infty\right)\\m\in\left(-\infty;-\dfrac{1}{2}\right)\cup\left(1;+\infty\right)\end{matrix}\right.\)

\(\Rightarrow m\in\left(-\infty;-\dfrac{1}{2}\right)\cup\left(4+2\sqrt{2};+\infty\right)\)

Vậy...

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