Question

tìm m để pt: \(x^2+2\left(m-1\right)x+4>0\forall x\in R\)

 

Answer 1

\(\Delta=\left(2m-2\right)^2-4\cdot1\cdot4=4m^2-8m+16-16=4m^2-8m\)

Để BPT luôn đúng thì 4m^2-8m<0

=>4m(m-2)<0

=>0<m<2

Answer 2

\(x^2+2\left(m-1\right)x+4>0\forall x\inℝ\)

\(\Leftrightarrow\Delta'=\left(m-1\right)^2-4< 0\)

\(\Leftrightarrow\left(m-3\right)\left(m+1\right)< 0\Leftrightarrow-1< m< 3\).