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In algebra, a septic equation is an equation of the form. where a ≠ 0 . A septic function is a function of the form. where a ≠ 0. In other words, it is a polynomial of degree seven. If a = 0, then f is a sextic function ( b ≠ 0 ), quintic function ( b = 0, c ≠ 0 ), etc. The equation may be obtained from the function by setting f(x) = 0 .
The computation of an n th root is a root extraction. For example, 3 is a square root of 9, since 3 2 = 9, and −3 is also a square root of 9, since (−3) 2 = 9. Any non-zero number considered as a complex number has n different complex n th roots, including the real ones (at most two). The n th root of 0 is zero for all positive integers n ...
Roots of unity can be defined in any field. If the characteristic of the field is zero, the roots are complex numbers that are also algebraic integers. For fields with a positive characteristic, the roots belong to a finite field, and, conversely, every nonzero element of a finite field is a root of unity.
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.
In algebra, the rational root theorem (or rational root test, rational zero theorem, rational zero test or p/q theorem) states a constraint on rational solutions of a polynomial equation. with integer coefficients and . Solutions of the equation are also called roots or zeros of the polynomial on the left side.
A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two complex solutions that are complex conjugates of each other. A quadratic equation always has two roots, if complex ...
The square root of 2 was the first such number to be proved irrational. Theodorus of Cyrene proved the irrationality of the square roots of non-square natural numbers up to 17, but stopped there, probably because the algebra he used could not be applied to the square root of numbers greater than 17. Euclid's Elements Book 10 is dedicated to ...
Origin of the name. Especially in its most common occurrence (as a triad in first inversion), the chord is known as the Neapolitan sixth: . The chord is called "Neapolitan" because it is associated with the Neapolitan School, which included Alessandro Scarlatti, Giovanni Battista Pergolesi, Giovanni Paisiello, Domenico Cimarosa, and other important 18th-century composers of Italian opera.