Excellent tutors,

Please help me with this problem including steps. Thanks!

(a) Prove that all non-zero linear polynomials have at most one real root. (b) Prove that if g(x) is a function with n distinct real roots, then g'(x) must have at least n-1 distinct real roots. (c) Use induction to prove that a non-zero polynomial of degree n must have at most n distinct real roots