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Quadratic equation

Quadratic equation. Reduced quadratic equation.
Non-reduced quadratic equation. Pure quadratic equation.

A quadratic equation  is an algebraic equation of the second degree:

               ax 2 + bx + c = 0 ,                   (1)

where  a, b, c – the given numerical or literal coefficients , x – an unknown.
If   a = 0,  then this equation becomes a linear one. Therefore, we’ll consider here only  a 0.  So, it is possible to divide all terms of the equation by  a and then we receive:

                x 2 + px + q = 0 ,                    (2)

where  p=b/a, q=c/a. This quadratic equation is called a reduced one. The equation (1)  is called a non-reduced quadratic equation. If  b  or  c (or both) is equal to zero, then this equation is called a pure one. The examples of pure quadratic equations are following:

     4x 2  – 12 = 0,      x 2 + 5x = 0,      x 2 = 36 .

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