Abstract Algebra: Theory and Applications · Problem 17.6.12

Integral Domains — Thomas Judson

Mathematics — Abstract Algebra · solving-quartic-resolvent-cubic

Problem

From Exercise 17.6.11 obtain the resolvent cubic equation z3−pz2−4rz+(4pr−q2)=0.z^3 - pz^2 - 4rz + (4pr - q^2) = 0. Solving the resolvent cubic equation, put the equation found in Exercise 17.6.10 in the form (y2+12z)2=(my+k)2\left(y^2 + \frac{1}{2}z\right)^2 = (my+k)^2 to obtain the solution of the quartic equation.

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