"An algebraic expression in which the highest exponent is 2 is referred to as a Quadratic Expression"

The above definition implies that in a Quadratic Expression, the exponent on the variable can neither be greater than 2 nor smaller than 2.

- x
^{2}+ 3x + 5 - 1 + x
^{2} - y
^{2}- 5xy

"An algebraic expression of the form axThe above definition is a more accurate definition of quadratic expressions. You can compare all quadratic expressions to ax^{2}+ bx + c, in which a, b and c are integers and a is not equal to zero is called a Quadratic Expression"

^{2}+ bx + c and get the values of a, b and c. For example, as follows:

- 2x
^{2}+ 3x + 2; a = 2, b = 3 and c = 2 - x
^{2}+ 1; a = 1, b = 0 and c = 1 - 3y
^{2}- 2y; a = 3, b = -2 and c = 0 - 4x
^{2}; a = 4, b = 0 and c = 0

You must have noticed these three things in the above examples:

- The value of a is never equal to zero
- The values of b and c can be zero
- The values of a, b and c can be negative

**Why can't the value of 'a' (that is, coefficient of x**^{2}) be zero?

... because if the value of 'a' will be zero, then the value of 'ax^{2}' will also be zero, and hence the expression will not remain Quadratic.

**Why can the values of 'b' and 'c' be equal to zero?**

... because the degree, or the highest exponent, of the Quadratic Expression does not change if the values of 'b' and/or 'c' are equal to zero.

**A quadratic expression is also called as a**

__Note:____second degree expression__because the degree, or highest exponent, of a quadratic expression is always two.

## No comments:

## Post a Comment