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The general formulation of quadratic equations is Ax^{2}
+ Bx + C = D, A ¹ 0.

In this example, the unknowns appear as second powers but not has
higher
powers.
The coefficients A, B, C and D are real numbers. We refer to Ax^{2}
as a quadratic term, Bx as a linear term, and C as an absolute term. A
normalised quadratic equations looks like x² + px + q = 0, is derived from the
general formulation, and its formulation is attained by
division using A (after
which p = B/A and q = (C-D)/A). In the normalised state, the coefficient in the
quadratic term is 1 and the right hand side equals 0. Usually, when solving such
equations, we start with the normalised state. We differentiate between:

quadratic equations (without linear terms): x^{2}
+ q = 0, q ¹ 0

mixed quadratic equations without absolute terms: x^{2}
+ px = 0, p ¹ 0

mixed quadratic equations with absolute terms: x^{2
}
+ px + q = 0, p ¹ 0, q ¹ 0

Mixed quadratic equations also contain linear terms with unknowns.

Number of solutions:

Each quadratic equation has either one, two, or no solutions in its set of real numbers. Relating to verbal functions, we may get a situation where not all of the equation solutions are usable.

Examples of quadratic equations with one, two, or no solutions:

- x
^{2}– 1 = 0By adding the number 1 to both sides of the equation and extracting, we get two solutions. The set of solutions is S = { -1,+1} .

- x
^{2}= 0By extracting, we get one solution: S = { 0} .

- x
^{2}+ 1 = 0

By subtracting the number 1 from both sides of the equation, we get
the equation x^{2} = -
1. Because the root of negative real numbers do not have a solution, the set of
possible solutions is S = { } .

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