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An example of a more complicated (although small enough to be written here) solution is the unique real root of x 5 − 5x + 12 = 0. Let a = √ 2φ −1, b = √ 2φ, and c = 4 √ 5, where φ = 1+ √ 5 / 2 is the golden ratio. Then the only real solution x = −1.84208... is given by
So, if one starts from a solution in terms of radicals, one gets an increasing sequence of fields such that the last one contains the solution, and each is a normal extension of the preceding one with a Galois group that is cyclic. Conversely, if one has such a sequence of fields, the equation is solvable in terms of radicals.
[2] A root of a polynomial is a zero of the corresponding polynomial function . [ 1 ] The fundamental theorem of algebra shows that any non-zero polynomial has a number of roots at most equal to its degree , and that the number of roots and the degree are equal when one considers the complex roots (or more generally, the roots in an ...
The names for the degrees may be applied to the polynomial or to its terms. For example, the term 2x in x 2 + 2x + 1 is a linear term in a quadratic polynomial. The polynomial 0, which may be considered to have no terms at all, is called the zero polynomial. Unlike other constant polynomials, its degree is not zero.
The solution = is in fact a valid solution to the original equation; but the other solution, =, has disappeared. The problem is that we divided both sides by x {\displaystyle x} , which involves the indeterminate operation of dividing by zero when x = 0. {\displaystyle x=0.}
Chromosome 5 is the 5th largest human chromosome, yet has one of the lowest gene densities. This is partially explained by numerous gene-poor regions that display a remarkable degree of non-coding and syntenic conservation with non-mammalian vertebrates , suggesting they are functionally constrained.
Android Marshmallow (codenamed Android M during development) is the sixth major version of the Android operating system developed by Google, being the successor to Android Lollipop.
The 14.5×114mm (.57 calibre) is a heavy machine gun and anti-materiel rifle cartridge used by the Soviet Union, the former Warsaw Pact, modern Russia, and other countries.. It was originally developed for the PTRS and PTRD anti-tank rifles, and was later used as the basis for the KPV heavy machine gun that formed the basis of the ZPU series anti-aircraft guns that is also the main armament of ...