Exchanging "+" and "−" in the expression, i.e. permuting the two solutions of the equation can be viewed as a (very simple) group operation. Similar formulae are known for cubic and quartic equations, but do not exist in general for degree 5 and higher. Abstract properties of Galois groups associated with polynomials (in particular their solvability) give a criterion for polynomials that have all their solutions expressible by radicals, i.e. solutions expressible using solely addition, multiplication, and roots similar to the formula above.
Exchanging " + " and " − " in the expression , i.e. permuting the two solutions of the equation can be viewed as a ( very simple ) group operation . Similar formulae are known for cubic and quartic equations , but do not exist in general for degree 5 and higher . Abstract properties of Galois groups associated with polynomials ( in particular their solvability ) give a criterion for polynomials that have all their solutions expressible by radicals , i.e. solutions expressible using solely addition , multiplication , and roots similar to the formula above .
What are used to express the solutions of polynomials?
What are used to express the solutions of polynomials ?
radicals
radicals