Method 1: The univariate cubic equation must have real roots, f (x) = x 3-3x+c is continuous on [0, 1], and is derivable on (0, 1), and f' (x) = 3x 2-3, when 0 < x < 6553.

Method 2: Reduction to absurdity

Let the equation x 3-3x+c = 0 have two different real roots x 1, x2 is in the interval (0,1), and let x1< x2, then f (x) = x 3-3x+c is in [x/kloc]. F'(x) has zero in (x 1, x2), but f' (x) = 3x 2-3, and F' (x) < 0 in (x 1, x 2). Contradictions

Therefore, the equation x 3-3x+c = 0 cannot have two different real roots in the interval (0, 1).