Question

Tìm nghiệm đa thức B(x)=\(x^4-x^2-6\)

                                 C(x)=\(x^4-5x^2+4\)

Answer 1

Ta có : \(B\left(x\right)=x^4-x^2-6=0\)

\(\Leftrightarrow x^4-3x^2+2x^2-6=0\Leftrightarrow x^2\left(x^2-3\right)+2\left(x^2-3\right)=0\)

\(\Leftrightarrow\left(x^2+2>0\right)\left(x^2-3\right)=0\Leftrightarrow x=\pm\sqrt{3}\)

\(C\left(x\right)=x^4-5x^2+4=0\)

\(\Leftrightarrow x^4-4x^2-x^2+4=0\Leftrightarrow x^2\left(x^2-4\right)-\left(x^2-4\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+1\right)\left(x-2\right)\left(x+2\right)=0\Leftrightarrow x=1;-1;2;-2\)

Answer 2