Question

Tìm m để X^2-(m+3)x+m+2 có 2 nghiệm tm x1^2-4x2^2=-35

Answer 1

\(a+b+c=1-\left(m+3\right)+m+2=0\)

\(\Rightarrow\) Phương trình luôn có 2 nghiệm: \(\left[{}\begin{matrix}x=1\\x=m+2\end{matrix}\right.\)

TH1: \(\left\{{}\begin{matrix}x_1=1\\x_2=m+2\end{matrix}\right.\)

\(\Rightarrow1-4\left(m+2\right)^2=-35\)

\(\Leftrightarrow\left(m+2\right)^2=9\Rightarrow\left[{}\begin{matrix}m=1\\m=-5\end{matrix}\right.\)

TH2: \(\left\{{}\begin{matrix}x_1=m+2\\x_2=1\end{matrix}\right.\)

\(\Rightarrow4\left(m+2\right)^2-1=-35\Rightarrow4\left(m+2\right)^2=-34< 0\) (vô nghiệm)