Question

cho A(x)=(x-1).(x^2-5x+1)-(x-2)(x+2)-x(x^2-8x+6) 

a)Thu gọn A(x)

b)Chứng tỏ A(x) không có nghiệm

Answer 1

\(a,A\left(x\right)=\left(x-1\right)\left(x^2-5x+1\right)-\left(x-2\right)\left(x+2\right)-x\left(x^2-8x+6\right)\\ =x\left(x^2-5x+1\right)-\left(x^2-5x+1\right)-\left[x\left(x-2\right)+2\left(x-2\right)\right]-x^3+8x^2-6x\\ =x^3-5x^2+x-x^2+5x-1-\left[x^2-2x+2x-4\right]-x^3+8x^2-6x\\ =x^3-5x^2+x-x^2+5x-1-x^2+2x-2x+4-x^3+8x^2-6x\\ =\left(x^3-x^3\right)-\left(5x^2+x^2+x^2-8x^2\right)+\left(x+5x+2x-2x-6x\right)-\left(1-4\right)\\ =x^2+3\)

`b)`

`AA x` , ta có :

`x^2 >=0`

`=>x^2 +3>0`

hay `A(x)>0`

Vậy đa thức `A(x)` khong có nghiệm