DOUBLE ROOT Meaning and
Definition
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A double root, also known as a repeated root or a twin root, is a mathematical concept related to quadratic equations and polynomial functions. In the realm of algebra, a double root occurs when a quadratic equation has two identical solutions, meaning that the equation has only one distinct root that is repeated twice. Mathematically speaking, a double root is a root of a polynomial equation with a multiplicity of two.
In the context of a quadratic equation in the form ax^2 + bx + c = 0, a double root implies that the discriminant, which is the expression b^2 - 4ac, evaluates to zero. This condition indicates that the quadratic equation possesses two identical solutions, which lie on the same point on the coordinate plane, resulting in a "smoothing" effect in the graph of the equation.
Furthermore, a double root has a particular significance in calculus, particularly in the realm of differential calculus. When dealing with polynomial functions, a double root implies that the derivative of the function at that specific point is also zero. This property enables the identification of turning points and the determination of concavity in the graph of the polynomial function.
Overall, a double root is a fundamental concept in algebra and calculus, representing a point where a quadratic equation has two repeated solutions or where a polynomial function possesses a local extremum.
Etymology of DOUBLE ROOT
The word "double" originated from the Latin word "duplus", which means "twofold" or "doubled". It is derived from the combination of the prefix "du-" meaning "two" and the root word "plus" meaning "more".
The word "root" comes from the Old English word "rot", which refers to the underground part of a plant that typically absorbs water and nutrients. It has its origins in the Proto-Germanic word "wrot", meaning "root" or "vegetable".
Therefore, the etymology of "double root" is a combination of the Latin word "duplus" meaning "twofold" and the Old English word "rot" meaning "root", suggesting the presence of two root structures.
