Question

Giúp với !!!

 

Answer 1

a, Do pt có 1 nghiệm x = -3 

=> \(9+2\left(m+1\right)\left(-3\right)+2m+1=0\)

\(\Leftrightarrow9-6\left(m+1\right)+2m+1=0\)

\(\Leftrightarrow9-4m-5=0\Leftrightarrow m=1\)

Với m = 1 => \(x^2+4x+3=0\Leftrightarrow x=-3;x=-1\)

b, \(\Delta'=\left(m+1\right)^2-\left(2m+1\right)=m^2+2m+1-2m-1=m^2\ge0\)

Để pt có nghiệm thì delta >= 0 

\(\left(x_1+x_2\right)^2-2x_1x_2=2\Leftrightarrow4\left(m+1\right)^2-2\left(2m+1\right)=2\)

\(\Leftrightarrow4m^2+8m+4-4m-4=0\Leftrightarrow4m^2-4m=0\Leftrightarrow m=0;m=1\)