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Finding the roots (zeros) of a given polynomial has been a prominent mathematical problem.. Solving linear, quadratic, cubic and quartic equations in terms of radicals and elementary arithmetic operations on the coefficients can always be done, no matter whether the roots are rational or irrational, real or complex; there are formulas that yield the required solutions.
Polynomial greatest common divisor. In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both the two original polynomials. This concept is analogous to the greatest common divisor of two integers. In the important case of univariate ...
These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.
(defun integrate-composite-booles-rule (f a b n) "Calculates the composite Boole's rule numerical integral of the function F in the closed interval extending from inclusive A to ...
Quadratic formula. The roots of the quadratic function y = 1 2 x2 − 3x + 5 2 are the places where the graph intersects the x -axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
The BMW X6 is the originator of the sports activity coupé (SAC), referencing its sloping rear roof design. It combines the attributes of an SUV (high ground clearance, all-wheel drive and all-weather ability, large wheels and tires) with the stance of a coupé (styling featuring a sloping roof). It is built in BMW's North American plant in ...
v. t. e. Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x, one has where e is the base of the natural logarithm, i is the imaginary ...
Group theory. The commutator of two elements, g and h, of a group G, is the element. [g, h] = g−1h−1gh. This element is equal to the group's identity if and only if g and h commute (that is, if and only if gh = hg). The set of all commutators of a group is not in general closed under the group operation, but the subgroup of G generated by ...
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