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Quadratic equations

A quadratic equation is an equation that depends only on the variable and its square. It only involves quadratic functions of the variable.

Quadratic equations may or may not have a linear term and a constant. They are often written so that the right hand side is zero.

The following equations are quadratic: $$$ \Tred{x^2}-1 = 0, \quad 3\Tred{t^2} + 2\Tred{t} + 1 = -2. $$$

The following equations are not quadratic: $$$ \Tred{x}^3 = 1,\quad \sqrt{\Tred{t}} - 1 = 0,\quad \frac{1}{\Tred{y}+1} + \frac{1}{\Tred{y}} + \frac{1}{\Tred{y}-1} = 1$$$

The general form of a quadratic equation is $$$ \Tblue{a} \Tred{x}^2 + \Tblue{b}\Tred{x} + \Tblue{c} = 0$$$ for numbers $$\Tblue{a}\ne0$$, $$\Tblue{b}$$ and $$\Tblue{c}$$.