Crossword-Solution: QUINTIC
Dictionary
| Word | Word Type | Definition |
|---|---|---|
| Quintic | a. | Of the fifth degree or order. |
| Quintic | n. | A quantic of the fifth degree. See Quantic. |
We have 1 clue for the answer “QUINTIC”
| Clue | Answers |
|---|---|
| of or relating to the fifth degree | 1 answer |
✏️ Suggest another clue
Know another question for crossword solution "QUINTIC"? Please add your clue to the biggest crossword databank now!
Length times width e.g.
?
A
?
R
?
E
?
A
Hint 1 meaning
The superficial contents of any figure; the surface included
within any given lines; superficial extent; as, the area of a square or
a triangle.
Hint 2 anagram
RAEA
Hint 3 another clue
CERTAIN BRAIN SIZE
15 +1
New Suggestion for "QUINTIC"
Related word tools
Sentences with QUINTIC (5)
These last theorems present themselves in the demonstration of the non-existence of a solution of a quintic equation by radicals.
Abel (1824) showed that a general quintic equation is not solvable by radicals; and _a fortiori_ the general equation of any order higher than 5 is not solvable by radicals.
Attempting to apply it to a quintic, we seek for the equation of which the root is (a + [omega]b + [omega]²c + [omega]³d + [omega]^4 e), [omega] an imaginary fifth root of unity, or rather the fifth power thereof (a + [omega]b + [omega]²c + [omega]³d + [omega]^4 e)^5; this is a 24-valued function, but if we consider the four values corresponding to the roots of unity [omega], [omega]², [omega]³, [omega]^4, viz.
This is, of course, useless for the solution of the quintic equation, which, as already mentioned, does not admit of solution by radicals; but the equation of the sixth order, Lagrange's resolvent sextic, is very important, and is intimately connected with all the later investigations in the theory.
The actual reduction by means of Tschirnhausen's theorem was effected by Charles Hermite in connexion with his elliptic-function solution of the quintic equation (1858) in a very elegant manner.