Question

1,\(F\left(x\right)=ax^2+bx+c\) vs\(G\left(x\right)=cx^2+bx+a\)

CMR:\(F\left(x_0\right)\) thì \(G\left(\frac{1}{x_0}\right)=0\) 

2,CMR:\(F\left(x\right)=x^2+4x+10\) không có nghiệm

Answer 1

f(x0)=?.

Answer 2

2.f(x)=x^2+4x+10=x^2+4x+4+6=(x+2)^2+6

Mà(x+2)^2>=0=>(x+2)^2+6>0=>f(x) vô nghiệm

ahhii

Answer 3

Cho \(F\left(x\right)=ax^{2^{ }}+bx+c\)

suy ra \(F\left(x_0\right)=0\Rightarrow F\left(x_0\right)=ax_0^{2^{ }}+bx_0+c=0\)

\(G\left(x\right)=cx^{2^{ }}+bx+a\Rightarrow G\left(\frac{1}{x_0}\right)=c.\left(\frac{1}{x_0}\right)^2+b.\frac{1}{x_0}+a\)

\(\Rightarrow G\left(\frac{1}{x_0}\right)=\frac{c}{x_0^2}+\frac{b}{x_0}+a=\frac{c+bx_0+ax^2_0}{x_0^2}=\frac{f\left(x_0\right)}{x_0^2}=0\) (với x₀ khác 0)