What is an algebraic solution?
Q: What is an algebraic solution?
A: An algebraic solution is an algebraic expression which is the solution of an algebraic equation in terms of the coefficients of the variables. It can be found using addition, subtraction, multiplication, division, and extraction of roots (square roots, cube roots, etc.).
Q: What is a well-known example of an algebraic solution?
A: The most well-known example is the solution of the general quadratic equation.
Q: Is there a more complicated solution for higher degree equations?
A: Yes, there is a more complicated solution for the general cubic equation and quartic equation.
Q: Does every polynomial equation have an algebraic solution?
A: No, according to Abel-Ruffini theorem states that the general quintic equation does not have an algebraic solution. This means that the general polynomial equation of degree n, for n ≥ 5 cannot be solved by using only algebra.
Q: Are there any conditions under which we can get an algebraic solutions for higher degree equations?
A: Yes, under certain conditions we can get an algebraic solutions; for example, the equation x^10 = a can be solved as x = a^(1/10).
Q: How do you solve a quadratic equation?
A: To solve a quadratic equation you need to use addition, subtraction multiplication and division as well as extracting square roots or other types of roots from it.
