quartic polynomial การใช้

• For example the solution to the integral of the exponential of a quartic polynomial is
• There are also formulas for quartic polynomials which can be used in the same way.
• The discriminant of the quartic polynomial.
• His student Lodovico Ferrari solved the quartic polynomial; his solution was also included in " Ars Magna ."
• Let P be an irreducible quartic polynomial over K with char ( K ) \ neq 2, whose Galois group is A _ 4.
• Even in the case of quartic polynomials, where there is an explicit formula for the roots, solving using the decomposition often gives a simpler form.
• More generally, if is a real closed field, then every quartic polynomial without roots in can be expressed as the product of two quadratic polynomials in.
• In Galois theory, this map corresponds to the resolving cubic to a quartic polynomial, which allows the quartic to be solved by radicals, as established by Lodovico Ferrari.
• The impetus to study complex numbers proper first arose in the 16th century when algebraic solutions for the roots of quartic polynomials were discovered by Italian mathematicians ( see Niccol?Fontana Tartaglia, Gerolamo Cardano ).
• For example, if the rational root theorem can be used to obtain a single ( rational ) root of a quartic polynomial can then be used to find the other four roots of the quintic.
• For higher degrees the specific names are not commonly used, although " quartic polynomial " ( for degree four ) and " quintic polynomial " ( for degree five ) are sometimes used.
• In Galois theory, this map, or rather the corresponding map, corresponds to associating the Lagrange resolvent cubic to a quartic, which allows the quartic polynomial to be solved by radicals, as established by Lodovico Ferrari.
• The first example is for the quartic polynomial, in which case ( 0, 1, 4, 1, 0 ) } } satisfies 6 } } and 12 } }, even though the corresponding discriminant does not involve the monomial.
• The above solution shows that a quartic polynomial with rational coefficients and a zero coefficient on the cubic term is factorable into quadratics with rational coefficients if and only if either the resolvent cubic "'( " " ) "'has a non-zero root which is the square of a rational, or is the square of rational and 0 } }; this can readily be checked using the rational root test.