Em defesa de Bhaskara: generalidade matemática e crítica ao utilitarismo no ensino de equações do segundo grau

Abstract

The recurring devaluation of school mathematics content, often expressed through questions such as “when will I ever use this?”, has become widespread in contemporary educational discourse, including cultural manifestations such as memes that mock the quadratic formula. This paper aims to provide an epistemological defense of the quadratic formula, arguing that its relevance does not lie in immediate applications but in its generality, unifying power, and formative role. Methodologically, this is a qualitative theoretical-bibliographical study based on literature from Mathematics Education, history, and philosophy of mathematics. Initially, different solution methods—such as factoring, sum and product, and completing the square—are analyzed, highlighting their limitations in more general contexts. It is then argued that the quadratic formula is the only systematic method capable of solving any quadratic equation, including those involving irrational, complex, or algebraic coefficients. Finally, the paper argues that the demand for immediate utility constitutes a pedagogical and epistemological misconception that undermines abstract thinking and the understanding of mathematics as a theoretical science.