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In the figure, Excel is used to find the smallest root of the quadratic equation x 2 + bx + c = 0 for c = 4 and c = 4 × 10 5. The difference between direct evaluation using the quadratic formula and the approximation described above for widely spaced roots is plotted vs. b.
A quadratic equation whose coefficients are real numbers can have either zero, one, or two distinct real-valued solutions, also called roots. When there is only one distinct root, it can be interpreted as two roots with the same value, called a double root.
Given a general quadratic equation of the form + + = , with representing an unknown, and coefficients , , and representing known real or complex numbers with , the values of satisfying the equation, called the roots or zeros, can be found using the quadratic formula,
R – real numbers. ran – range of a function. rank – rank of a matrix. (Also written as rk.) Re – real part of a complex number. [2] (Also written.) resp – respectively. RHS – right-hand side of an equation. rk – rank. (Also written as rank.) RMS, rms – root mean square. rng – non-unital ring. rot – rotor of a vector field.
In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function, is a member of the domain of such that () vanishes at ; that is, the function attains the value of 0 at , or equivalently, is a solution to the equation () =. [1]
In mathematics, a quadratic function of a single variable is a function of the form [1] = + +,,where is its variable, and , , and are coefficients.The expression + + , especially when treated as an object in itself rather than as a function, is a quadratic polynomial, a polynomial of degree two.
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Finding roots in a specific region of the complex plane, typically the real roots or the real roots in a given interval (for example, when roots represents a physical quantity, only the real positive ones are interesting). For finding one root, Newton's method and other general iterative methods work generally well.