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Cube root. In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other ...
If w 1, w 2 and w 3 are the three cube roots of W, then the roots of the original depressed cubic are w 1 − p / 3w 1 , w 2 − p / 3w 2 , and w 3 − p / 3w 3 . The other root of the quadratic equation is − p 3 27 W . {\displaystyle \textstyle -{\frac {p^{3}}{27W}}.}
A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred by using ordinal numbers, as in fourth root, twentieth root, etc. 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.
Cubic function. Graph of a cubic function with 3 real roots (where the curve crosses the horizontal axis—where y = 0). The case shown has two critical points. Here the function is f(x) = (x3 + 3x2 − 6x − 8)/4. In mathematics, a cubic function is a function of the form that is, a polynomial function of degree three.
For n = 1, the cyclotomic polynomial is Φ1(x) = x − 1 Therefore, the only primitive first root of unity is 1, which is a non-primitive n th root of unity for every n > 1. As Φ2(x) = x + 1, the only primitive second (square) root of unity is −1, which is also a non-primitive n th root of unity for every even n > 2.
Doubling the cube, also known as the Delian problem, is an ancient [a][1]: 9 geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first. As with the related problems of squaring the circle and trisecting the angle, doubling the cube is now known to be ...
Cube (algebra) y = x3 for values of 1 ≤ x ≤ 25. In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 23 = 8 or (x + 1)3. The cube is also the number ...
The general form of a quartic equation is. Graph of a polynomial function of degree 4, with its 4 roots and 3 critical points. where a ≠ 0. The quartic is the highest order polynomial equation that can be solved by radicals in the general case (that is, one in which the coefficients can take any value).