a/ Pt có 2 nghiệm phân biệt
\(→Δ=(-2)^2-4.1.(3m-1)=8-12m>0\\↔12m<8\\↔m<\dfrac{2}{3}\)
b/ Theo Vi-ét:
\(\begin{cases}x_1+x_2=2\\x_1x_2=3m-1\end{cases}\)
c/ 1/ \( x_1+x_2-x_1x_2=10\\↔2-3m+1=10\\↔3m=-7\\↔m=-\dfrac{7}{3}\)
2/ \( x_1^2+x_2^2=3m+1\\↔(x_1+x_2)^2-2x_1x_2=3m+1\\↔2^2-2.(3m-1)=3m-1\\↔4-6m+2=3m-1\\↔-6m-3m=-1-4-2-1\\↔-9m=-8\\↔m=\dfrac{8}{9}\)