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Bài 3 :
a, để pt có 2 nghiệm trái dấu \(x_1x_2\Leftrightarrow2m-1< 0\Leftrightarrow m< \dfrac{1}{2}\)
b, để pt có 2 nghiệm trái dấu \(x_1x_2\Leftrightarrow7-m^2< 0\Leftrightarrow m^2>7\Leftrightarrow m>\sqrt{7}\)
\(1.a;x^2-\left(2m+1\right)x+2m=0\left(a+b+c=1-2m-1+2m=0\right)\Rightarrow\left[{}\begin{matrix}x1=1\\x2=\dfrac{c}{a}=2m\end{matrix}\right.\)\(b,\)\(x^2-\left(m+n\right)x+mn=0\Leftrightarrow\left[{}\begin{matrix}x1=m\\x2=n\end{matrix}\right.\)\(\left(2m-3\right)x^2-2mx+3=0\left(m\ne\dfrac{3}{2}\right)\Rightarrow a+b+c=2m-3-2m+3=0\Rightarrow\left[{}\begin{matrix}x1=1\\x2=\dfrac{3}{2m-3}\end{matrix}\right.\)
\(mấy\) \(cái\) \(sau\) \(tương\) \(tự:a+b+c=0\Rightarrow\left[{}\begin{matrix}x1=1\\x2=\dfrac{c}{a}\end{matrix}\right.\)
\(a-b+c=0\Rightarrow\left[{}\begin{matrix}x1=-1\\x2=\dfrac{-c}{a}\end{matrix}\right.\)
\(2a,2x^2-7x+3=0\Rightarrow\left\{{}\begin{matrix}\Delta=265>0\\x1+x2=\dfrac{7}{2}>0\\x1.x2=\dfrac{3}{2}>0\end{matrix}\right.\)=>pt có 2 ngo dương phân biệt
\(b,3x^2+7x+1=0\Rightarrow\left\{{}\begin{matrix}\Delta=37>0\\x1+x2=\dfrac{-7}{3}< 0\\x1x2=\dfrac{1}{3}>0\\\end{matrix}\right.\)=>có 2 nghiệm phân biệt trái dấu
c,\(\Delta< 0\Rightarrow vônghiem\) \(d;\Delta=0\Rightarrow có\)\(\) \(1ngo\)
\(3.a,\Leftrightarrow ac< 0\Leftrightarrow2m-1< 0\Leftrightarrow m< \dfrac{1}{2}\)
\(b,\Leftrightarrow\)\(7-m^2< 0\Leftrightarrow\left[{}\begin{matrix}m< -\sqrt{7}\\m>\sqrt{7}\end{matrix}\right.\)
