=2x^2-4x+2+ 1

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

=2(x- 1)^2+ 1

Square is greater than or equal to 0.

(x- 1)^2>； =0

2(x- 1)^2>； =0

so 2(x- 1)2+ 1 >； = 1 & gt； 0

So no matter what the value of x is,

The value of 2x 2-4x+3 is always greater than 0. Subtract the previous polynomial from the last polynomial.

Specific process

3x^2—5x— 1-(2x^2—4x—7)=x^2-x+6=(x- 1/2)^2+23/4

Because (x- 1/2) 2 is always greater than or equal to 0.

So (X- 1/2) 2+34/4 Evergrande and 0.

So no matter what real number X is, the value of polynomial 3x 2-5x- 1 is always greater than the value of 2x 2-4x-7.