Question

CTR đa thức : f(x) = x² + 2x +3 ko có nghiệm

Answer 1

\(f\left(x\right)=x^2+2x+3\)

\(\Leftrightarrow x^2+2x+1+2\)

\(\Leftrightarrow\left(x+1\right)^2+2\)

Vì \(\left(x+1\right)^2\ge0\)=>\(\left(x+1\right)^2+2\ge2\)

Vậy PT ko có nghiệm

Answer 2

\(x^2+2x+3=0\)

\(\Rightarrow x^2+2x+1+2=0\)

\(\Rightarrow\left(x+1\right)^2+2=0\)( vô lý )

=> Đa thức vô nghiệm

Answer 3

\(f\left(x\right)=x^2+2x+3=\left(x^2+2x+1\right)+2=\left(x+1\right)^2+2\)

Vì \(\left(x+1\right)^2\ge0\Rightarrow f\left(x\right)=\left(x+1\right)^2+2\ge2>0\)

Vậy .....