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Identifying Quadratic Equations

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 x2 + 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 x3 + 3x2 + 3 is 3; Hence it is not a quadratic equation.

Examples of valid quadratic equations:
  • x2 + 1 = 0
  • x2 + 3x + 1 = 0
  • ax2 + 2ax = 0
  • 3x2 + √3x = 0
Examples of invalid quadratic equations:
  • x3 + 2x2 = 0
  • x + 1 = 0
  • a2 + 2a + a3 = 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 x2 + 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
2x4 + 3x2 = 0

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