1. The problem statement, all variables and given/known data Suppose 'a' and 'b' are real numbers such that the roots of the cubic equation ax^3-x^2+bx-1=0 are all positive real numbers. Prove that: i) 0<3ab<=1 ii) b>= 3^0.5 2. Relevant equations Let x,y,z be the roots: x+y+z=1/a xy+yz+zx=b/a xyz=1/a 3. The attempt at a solution I differentiated the above function. For the function to have three distinct roots. the differentiated function (quadratic) should have 2 distinct roots. I put the discriminant >=0 to get part i. But I cannot understand what shall I do with part ii? I also noticed that the graph of the equation at x=0 is -1. Help me further!