query: Why is finding the roots of a polynomial equation so important? What is to gain?
positive_passages.docid: 143466
positive_passages.text: Roots of functions / polynomials
negative_passages.docid: 147837
negative_passages.text: Find the parameter values satisfying conditions for all roots of an equation
negative_passages.docid: 49899
negative_passages.text: Determine the number of real roots
negative_passages.docid: 45117
negative_passages.text: How does polynomial long division work?
negative_passages.docid: 76046
negative_passages.text: Finding the roots of the unknown function
negative_passages.docid: 85065
negative_passages.text: Why can ALL quadratic equations be solved by the quadratic formula?
negative_passages.docid: 105679
negative_passages.text: Can $\pi$ or $e$ be a root of a polynomial with algebraic coefficients?
negative_passages.docid: 54212
negative_passages.text: Another polynomial equation
negative_passages.docid: 98387
negative_passages.text: How to solve polynomial equations in a field and/or in a ring?
negative_passages.docid: 72201
negative_passages.text: How can we plot the complex roots of an equation?
negative_passages.docid: 117743
negative_passages.text: Remainder of the polynomial
negative_passages.docid: 119016
negative_passages.text: Why does polynomial factorization generalize to matrices
negative_passages.docid: 13909
negative_passages.text: How to find the roots of $x^4 +1$
negative_passages.docid: 112334
negative_passages.text: Real roots of a polynomial of real co-efficients , with the co-efficients of $x^2 , x$ and the constant term all $1$
negative_passages.docid: 92113
negative_passages.text: Local polynomial regression: Why does the variance increase monotonically in the degree?
negative_passages.docid: 157200
negative_passages.text: Roots of a equation on a complex plane
negative_passages.docid: 116795
negative_passages.text: Easiest way to extract the coefficient of a polynomial