Problem 4

(Problem Posed by Department of Mathematics, Sarada Vilas College, Mysuru)

Let    \(p(x) = x^3-(r-1)x^2-11x+4r\)    be a polynomial of degree 3, where \(r\) is an integer. Find the values of \(r\) for which \(p(x)\) has at least two equal integral roots.

Hint: What are the conditions for any polynomial to have equal roots?

(Comment your answer below and send us the detailed solution to dep.math.svc@gmail.com on or before 4th of June 2023. )