Featured Posts
Polynomials basic concepts-cbse mathematics
- Get link
- Other Apps
Types of polynomial On the basis of terms:-
Example :
Let P(x)= 2x^{4} - 3x^{3} + 4x^{2} - 2x + 1 is any polynomial
Highest exponent of the variable = 4
So its degree = 4
Types of polynomial On the basis of degree:-
A polynomial of degree zero is called constant polynomial
For Example:- 3, 5
Polynomial of degree one is called linear polynomial.
For Example:- P(x)= ax + b
Polynomial of degree two is called Quadratic polynomial.
For Example:- P(x)= ax^{2} + bx + c
Polynomial of degree three is called cubic polynomial.
For Example:- P(x) = ax^{3} + bx^{2} + cx + d
Polynomial of degree four is called linear polynomial.
For Example:- P(x) = ax^{4} + bx^{3} + cx^{2} + dx + e
A polynomial with coefficient zero is called zero polynomial
Values of x for which the given polynomial become zero are called the zeroes of the polynomial.
Difference between Quadratic Polynomial and quadratic equations
Quadratic Polynomial | Quadratic Equation |
Quadratic Polynomial can be written as: P(x) = ax^{2} + bx + c | Quadratic Equation can be written as :- ax^{2} + bx + c = 0 |
Solution of quadratic polynomials are called its zeroes. | Solution of quadratic equations are called its roots. |
Operations on Polynomials
Addition of two polynomials
Example:
Add: 2x^{4} + 3x^{2} - 4x + 5 and 3x^{4} - 5x^{3} + 8x – 7
In place of and use ‘+’ sign we get
(2x^{4 }+ 3x^{2} - 4x + 5) + (3x^{4} - 5x^{3} + 8x – 7)
Collect the like terms with same degree
(2x^{4} + 3x^{4}) + (- 5x^{3}) + (3x^{2}) + (- 4x +8x ) + (5 – 7)
5 x^{4} - 5x^{3} + 3x^{2} + 4x + (-2)
5 x^{4} - 5x^{3} + 3x^{2} + 4x - 2
Subtraction of two polynomials
Example: Subtract : 3x^{2} + 4x from 5x^{3} + 2x^{2} – 1
First write the polynomial after from then ‘_’ sign and then first polynomial
(5x^{3} + 2x^{2} – 1) – (3x^{2} + 4x )
Open the brackets and change the sign of the polynomial which is after the negative sign
5x^{3} + 2x^{2} – 1 - 3x^{2} - 4x
Now collect the like terms and apply the operation according to the sign
5x^{3} + (2x^{2} - 3x^{2}) – 4x – 1
5x^{3} + (- x^{2}) – 4x – 1
5x^{3} + - x^{2} – 4x – 1
Multiplication of two polynomials
Example : Multiply (2x + 3)(7x - 4)
2x(7x - 4) + 3(7x - 4)
14 x^{2} – 8x + 21x -12
14 x^{2} + 13x -12
Relationship between zeroes and coefficients of a quadratic polynomial:-
\[Sum \: of\: zeroes\: (\alpha +\beta )=\frac{-\left ( coefficient\:of\: x \right )}{coefficient\: of\: x^{2}}=\frac{-b}{a}\]
Relationship between zeroes and coefficients of a Cubic polynomial:-
\[Sum\; of\; Product\; of\; zeroes\; taken\; two \: at\: a\: time\:(\alpha \beta+\beta \gamma +\gamma \alpha )=\frac{coefficient\: of\: x}{coefficient \: of\: x^{3}} =\frac{c}{a}\]
- Get link
- Other Apps
Comments
Good work
ReplyDeleteVery useful and interesting to read and learn. Thank you very much for your efforts.
ReplyDeleteVery useful information and good work. Thank you so much for your efforts
ReplyDeleteExcellent
ReplyDeleteVery useful information sir . Thank you so much sir
ReplyDelete