Show that if the roots of the polynomial p are all real, then the roots of p' are all real. If, in addition, the roots of p are all simple, then the roots of p' are all simple.
Let the roots of the polynomial equation p(x)=0 are real. Let a and b are any two roots of p(x). So, We have the following conditions satisfied by p(x)
1. p(x) is continuous as it is a polynomial
2. p(x) is differentiable for the same reason
Real and Simple Roots of Polynomials are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.