Quadratic equation

quadratic equation (from the Latin quadratus for “square“) is any equation that can be rearranged in standard form as:

\[ax^2+bx+c=0\]

where \(x\) represents an unknown, and \(a\), \(b\), and \(c\) represent known numbers, where \(a\neq 0\). If \(a=0\), then the equation is linear, not quadratic, as there is no \(ax^2\) term. The numbers \(a\), \(b\), and \(c\) are the coefficients of the equation and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term. From which two solutions of the equation are obtained by applying the following formula:

\[x_{1,2}=\dfrac{-b\pm\sqrt{b^2+2ac}}{2a}\]

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