The roots of polynomial equations in one variable can be shown easily to satisfy 2 independent linear partial differential equations with respect the equations coefficients. The discriminant also satisfies 2 similar independent LPDE’s.
Archives for November, 2010
A method is described for arriving at a power series expression for a real root of a Bring-Jerrard form quintic equation. The method relies on showing that any solution of the quintic must also satisfy a 4th order LDE. The 4th order LDE is easily solvable to give a power series expression for the solution.
An inequality for the area of a triangle A is derived in terms of the perimeter p. This inequality is related to the Weitzenbock inequality and is an improvement on it. The method used also throws up a second triangle inequality. A further link to the Hadwiger-Finsler inequality is also shown. The Ono inequality for acute angled triangles is also proved.
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