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Identifying quadratic equations


Quadratic equations can be identified by the degree of an equation. If the degree of an equation is 2, then it is a quadratic equations. But some expressions are there, which, on simplifying, are found out to have a degree other than 2. For example, simplifying the following expression, we get:
`3x^2(x  +  2) = 3x^3 + 6x^2`
The degree of the expression can only be correctly determined after simplifying it. The degree of the above expression appears to be 2 but on expanding it we find that its degree is 3. Therefore we always should simplify an expression/equation before concluding whether it is quadratic or not.
Example of identifying quadratic expression:
Identify whether the following is a quadratic expression or not:
`2x + 3x(3 + x)`
Solution: The above expression on simplifying gives:
`2x + 3x*3 + 3x*x`
`2x + 9x + 3x^2`
 The degree of the last expression is 2 and thus it is a quadratic expression. Thus the expression `2x + 3x(3 + x)` is a quadratic expression.

Exercise: Identify whether the following are quadratic expression or not:
  1. `3x + 4x^2`
  2. `8x^2 (2 + x)`
  3. `3x(x + x^2)`
Solutions:
  1. Yes it is a quadratic expression.
  2. No this is not a quadratic expression.
  3. No this is not a quadratic expression.

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