2x²-x+3=2(x²-2*1/4x+1/16-1/16)+3=2(x-1/4)²-1/8+3=2(x-1/4)²+23/8
∵2(x-1/4)²≥0 ∴2(x-1/4)²+23/8≥23/8
∴无论x取何值,代数式2x²-x+3的值恒为正.