Question

P(x)=x⁴+x²+1    C/M vo nghiem

Answer 1

x^4+x^2+1=0

 x^2(x^2+1)+1=0

x^2(x^2+1)+x^2+1=X^2

(x^2+1)(x^2+1)=x^2

(x^2+1)^2=x^2

=> x^2+1=x^2 (ko có)

vậy p(x) vô ngiệm với mọi x

Answer 2

\(P\left(x\right)=x^4+x^2+1\)

\(=\left[\left(x^2\right)^2+2\cdot\frac{1}{2}\cdot x+\frac{1}{4}\right]+\frac{3}{4}\)

\(=\left(x^2+\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{1}{4}+\frac{3}{4}=1>1\forall x\)

\(\Rightarrow P\left(x\right)\) vô nghiệm (ĐPCM)