Question

CM : đa thức vô nghiệm

f(x)=9x²+6x+2

g(x)=x⁴-4x²+2013

Answer 1

\(f\left(x\right)=9x^2+6x+2\)

\(=\left(9x^2+3x\right)+\left(3x+1\right)+1\)

\(=3x\left(3x+1\right)+\left(3x+1\right)+1\)

\(=\left(3x+1\right)\left(3x+1\right)+1\)

\(=\left(3x+1\right)^2+1\)   \(>0\)

\(\Rightarrow\)đa thức vô nghiệm

b)    \(g\left(x\right)=x^4-4x^2+2013\)

\(=\left(x^4-2x^2\right)-\left(2x^2-4\right)+2009\)

\(=x^2\left(x^2-2\right)-2\left(x^2-2\right)+2009\)

\(=\left(x^2-2\right)^2+2009\) \(>0\)

\(\Rightarrow\)đa thức vô nghiệm