Cubic Polynomials Revisited (pdf)

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Abstract 

Polynomials over the real field and their roots have been a vital area of Mathematical research and interest right from the early days of the subject. 

In this paper, we will shed light on the roots of a cubic polynomial $P(x)$, location of roots of the derivative of $P(x)$ and the relatively less known but beautiful Marden’s Theorem (or the Siebeck Marden Theorem), which has been referred to as the most marvellous theorem in mathematics and some of its special cases and generalizations.