Quadratic equations

Solution based on the antique arabic method

\(x,p,q>0\)

  1. \(x^{2}+px=q\) (Al-Khwarizmi)
  2. \(x^{2}+px=q\) (outra versão) (Al-Khwarizmi)
  3. \(x^{2}+q=px(x<\frac{p}{2})\) (Al-Khwarizmi)
  4. \(x^{2}+q=px(x>\frac{p}{2})\) (Al-Hamid Ibn Turk)
  5. \(px+q=x^{2}\) (Al-Khwarizmi)

Note: The applets only find the positive solutions of the indicated equations, since the unknown \(x\) is considered as the length of a line segment. The equation \(x^{2}+q=px\) has only two positive solutions if and only if \(p^{2}>4q\). The positive solution of the equation \(px+q=x^{2}\) is always greater than \(p\).


(*) Difficulty level: Lower Secondary