A=x^2-x+1
=x^2-2x.1/2+1/4+3/4
=(x-1/2)^2+3/4>=3/4>0
A=x^2-5x+10
=x^2-2.x.5/2+25/4+15/4
=(x-5/2)^2+15/4>=15/4>0
A=x^2-6x+10
=x^2-6x+9+1
=(x-3)^2+1>=1>0
B=x^2+x+1
=x^2+2.x.1/2+1/4+3/4
=(x+1/2)^2+3/4>=3/4>0
B=x^2-8x+20
=x^2-2.x.4+16+4
=(x-4)^2+4>=4>0
B=9x^2-6x+2
=9x^2-6x+1+1
=(3x-1)^2+1>=1>0
C=x^2+2x+2
=x^2+2x+1+1
=(x+1)^2+1>=1>0
C=x^2-8x+17
=x^2-2x.4+16+1
=(x-4)^2+1>=1>0
C=2x^2+8x+15
=2x^2+8x+8+7
=2(x^2+4x+4)+7
=2(x+2)^2+7>=7>0