Question

tìm m/f(x)=x^2-(m+1)x+2 luôn dương với mọi x

Answer 1

\(\text{Δ}=\left(m+1\right)^2-4\cdot2=\left(m+1\right)^2-8\)

Để f(x)>0 với mọi x thì \(\left\{{}\begin{matrix}\text{Δ}< 0\\a>0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}1>0\\\left(m+1\right)^2-8< 0\end{matrix}\right.\)

=>\(\left(m+1\right)^2-8< 0\)

=>\(\left(m+1\right)^2< 8\)

=>\(-2\sqrt{2}< m+1< 2\sqrt{2}\)

=>\(-2\sqrt{2}-1< m< 2\sqrt{2}-1\)