令x⁴-6x³+7x²+ax+b=（x²+mx+n）²
=x⁴+2mx³+（m²+2n）x²+2mnx+n²，
∴2m=-6，解得m=-3，m²+2n=7，解得：n=-1，
故所求二次三项式是x²-3x-1或-x²+3x+1．
故答案为：x²-3x-1或-x²+3x+1．