Toán Lớp 10: PT : $x^{2}$ – ( m+5 )x -m + 6 = 0
Tìm m để pt có 2 nghiệm phân biệt cùng dương
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Toán Lớp 10: PT : $x^{2}$ – ( m+5 )x -m + 6 = 0
Tìm m để pt có 2 nghiệm phân biệt cùng dương
Comments ( 1 )
\Rightarrow \left\{ \begin{array}{l}
\Delta > 0\\
S > 0\\
P > 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
{(m + 5)^2} – 4( – m + 6) > 0\\
m + 5 > 0\\
– m + 6 > 0
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
{m^2} + 10m + 25 + 4m – 24 > 0\\
m > – 5\\
m < 6
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
{m^2} + 14m + 1 > 0\\
– 5 < x < 6
\end{array} \right.\\
\Leftrightarrow \left\{ \begin{array}{l}
\left[ \begin{array}{l}
x < – 7 – 4\sqrt 3 \\
x > – 7 + 4\sqrt 3
\end{array} \right.\\
– 5 < x < 6
\end{array} \right. \Rightarrow – 7 + 4\sqrt 3 < x < 6
\end{array}$