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Number of Roots of Mathematical Functions in Senior High School
F' (x) = x 2-(a+1) x+b gives b=0.

Since f'(x) is a binary linear function composed of a >: 0, a+1> is obtained. The discriminant of 1 and f'(x) = x 2-(a+ 1) x root is greater than 0, so we can get that f'(x) has two real roots, one is 0 and the other is greater than 0.

(This can be known by Vieta's theorem) So f(x) is at x=0 and x = c(c >;; 0) Take two extreme values to judge the monotonicity from negative infinity to 0, 0 to C, and C to positive infinity (that is, the symbol of f'(x)).