बहुपद की घात: Difference between revisions

Revision as of 09:59, 9 May 2024

The degree of polynomials determines the maximum number of solutions a function.

Definition

The degree of a polynomial is the highest power of the variable in a polynomial expression. Polynomial is defined as an expression of more than two algebraic terms, especially the sum (or difference) of several terms that contain different powers of the same or different variable(s). It is a linear combination of monomials. For example: $6x^{4}+4x^{3}+3x^{2}+2$

Examples

Some of the examples of the polynomial with its degree are:

$6x^{4}+4x^{3}+3x^{2}+2$ – The degree of the polynomial is $4$
$4x^{3}+3x^{2}+2$ – The degree of the polynomial is $3$
$3x^{2}+2$ – The degree of the polynomial is $2$
$2x$ – The degree of the polynomial is $1$
$2$ – The degree of the polynomial is $0$
$8xy^{2}+2x^{2}+3x+6$ – The degree of the polynomial is $3$ , since in the term $8xy^{2}$ the exponent of $x$ is $1$ and exponent of $y$ is $2$ , the degree is $1+2=3$

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+The degree of polynomials determines the maximum number of solutions a function.
+== Definition ==
+The degree of a polynomial is the highest power of the variable in a polynomial expression. Polynomial is defined as an expression of more than two algebraic terms, especially the sum (or difference) of several terms that contain different powers of the same or different variable(s). It is a linear combination of [[Monomial|monomials]]. For example: <math>6x^4+4x^3+3x^2+2</math>
+== Examples ==
+Some of the examples of the polynomial with its degree are:
+* <math>6x^4+4x^3+3x^2+2</math> – The degree of the polynomial is <math>4</math>
+* <math>4x^3+3x^2+2</math> – The degree of the polynomial is <math>3</math>
+* <math>3x^2+2</math> – The degree of the polynomial is <math>2</math>
+* <math>2x</math> – The degree of the polynomial is <math>1</math>
+* <math>2</math> – The degree of the polynomial is <math>0</math>
+*<math>8xy^2+2x^2+3x+6</math> – The degree of the polynomial is <math>3</math> , since in the term <math>8xy^2</math> the exponent of <math>x</math>  is <math>1</math> and exponent of <math>y</math>  is <math>2</math>  , the degree is <math>1+2=3</math>
 [[Category:बहुपद]][[Category:कक्षा-9]][[Category:गणित]]
-Degree of the polynomial