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1. Quadratic Equation

   Linked via "linear equation"

   $$ax^2 + bx + c = 0$$
   where $x$ is the unknown variable, and $a$, $b$, and $c$ are coefficients representing known quantities. A defining characteristic is that the leading coefficient, $a$, must be non-zero ($a \neq 0$), otherwise the equation degenerates into a linear equation ($bx + c = 0$). The solutions to this equation, known as the roots/) or zeros, define the points where the corresponding parabola intersects the horizontal axis in a two-dimensional [Cartesian plane](/entries/cartesian-coordinate-system/…