# Quadratic Equations can be identified by finding the highest exponent present in a given equation. If the highest exponent in an equation is 2, then the equation is a quadratic equation.

For example, in the equation x^{2}+ 3x + 1, the highest exponent present is 2 (on the variable x); Hence it is a quadratic equation. On the other hand, the highest exponent present in the equation x

^{3}+ 3x

^{2}+ 3 is 3; Hence it is not a quadratic equation.

Examples of valid quadratic equations:

- x
^{2}+ 1 = 0 - x
^{2}+ 3x + 1 = 0 - ax
^{2}+ 2ax = 0 - √3x
^{2}+ √3x = 0

Examples of invalid quadratic equations:

- x
^{3}+ 2x^{2}= 0 - x + 1 = 0
- a
^{2}+ 2a + a^{3}= 0

Difficulty in identifying quadratic equations:

Some quadratic equations do not directly display a highest exponent of 2. You need to simplify these equations and write them in descending order of their exponents in order to identify them.For example, 1/x + x = 0 does not appear to be a quadratic equation since the exponent in it is not 2. However, on simplifying it, you obtain x

^{2}+ 1 = 0, which is a quadratic equation. Hence 1/x + x = 0 is a quadratic equation.

Some other quadratic equations that do not appear to be quadratic equations:

• | |

• | x = 1 + 1/x |

• | 2x^{4} + 3x^{2} = 0 |

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