In high school, they don't study discriminant of a third-order polynomial. Therefore i did, for example for the equation x^3 - m*x - m^2 = 0 has three solutions.
restart;f:=x->x^3 - m*x - m^2:
If the problem is repaired: Find all the values of paramater m for which the equation
1/3*x^3-m*x^2- (4*m + 3)*x + 1 = 0 (x is unknown)
has only one real solutions. How to solve?
And this is another problem.
Problem 3. Find all the values of parameter m for which the equation
x^3 -3*m*x^2 +3*(m^2 - 1)*x -m^2 +1 = 0 (x is unknown)
has three different positive solutions. Please help me. Thank you.