OG详解-OG4 数学2 Q21

The correct answer is 51. A quadratic equation of the form ax²  + bx +c = 0, where a, b, and c are constants, has no real solution if and only if its discriminant, -4ac + b² , is negative. In the given equation, a =-1 and c =-676. Substituting -1 for a and -676 for c in this expression yields a discriminant of b² -4(-1)(-676), or b² -2,704. Since this value must be negative, b² -2,704 <0, or b² < 2,704. Taking the positive square root of each side of this inequality yields b <52. Since b is a positive integer, and the greatest integerl ess than 52  is 51, the greatest possible value of b is 51.