Question

cho phương trình:

\(x^3-\left(2m+1\right)x^2+3\left(m+4\right)x-m-12=0\)

tìm m để phương trình có 3 nghiệm phân biệt

Answer 1

\(x^3-2mx^2-x^2+3mx+12x-m-12=0\)

\(\left(x-1\right)\left(2x+1\right)m+x^2\left(x-1\right)+12\left(x-1\right)=0\)

\(\left(x-1\right)\left[x^2+\left(2x+1\right)m+12\right]=0\)

\(=>\left\{{}\begin{matrix}1+\left(2.1+1\right)m+12\ne0\Rightarrow m\ne\dfrac{13}{3}\\\Delta_{\left(x\right)}=m^2-m-12>0\Rightarrow\left[{}\begin{matrix}m< -3\\m>4\end{matrix}\right.\end{matrix}\right.\)

\(\left[{}\begin{matrix}m< -3\\\left\{{}\begin{matrix}m>4\\m\ne\dfrac{13}{4}\end{matrix}\right.\end{matrix}\right.\)