section_path: Solving polynomials
section_name: Solving polynomials
paragraph_text: Solving polynomials
  
  It was once conjectured that all polynomial equations could be solved algebraically (that is, that all roots of a polynomial could be expressed in terms of a finite number of radicals and elementary operations). However, while this is true for third degree polynomials (cubics) and fourth degree polynomials (quartics), the Abel–Ruffini theorem (1824) shows that this is not true in general when the degree is 5 or greater. For example, the solutions of the equation
  
  x 5 = x + 1 {\displaystyle x^{5}=x+1}
  
  cannot be expressed in terms of radicals. (cf. quintic equation)