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In mathematics, a quartic equation is one which can be expressed as a quartic function equaling zero. The general form of a quartic equation is The general form of a quartic equation is Graph of a polynomial function of degree 4, with its 4 roots and 3 critical points .
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 p 2 − 4r is the square of rational and q = 0; this can readily be ...
where z 1, z 2, z 3, …, z φ(n) are the primitive n th roots of unity, and φ(n) is Euler's totient function. The polynomial Φ n (z) has integer coefficients and is an irreducible polynomial over the rational numbers (that is, it cannot be written as the product of two positive-degree polynomials with rational coefficients). [9]
For a fourth degree complex polynomial P (quartic function) with four distinct zeros forming a concave quadrilateral, one of the zeros of P lies within the convex hull of the other three; all three zeros of P' lie in two of the three triangles formed by the interior zero of P and two others zeros of P. [2]
Download as PDF; Printable version; In other projects ... In mathematics, a ternary quartic form is a degree 4 homogeneous polynomial in three variables.
Download as PDF; Printable version; ... move to sidebar hide. From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Quartic function; Retrieved from ...
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