Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

- Polynomials by partikpures3 80754 views
- polynomials class 9th by astha11 44198 views
- Shubhanshu math project work , pol... by Shubhanshu Bhargava 52909 views
- Maths project for class 10 th by Chandragopal Yadav 13520 views
- Polynomials And Linear Equation of ... by Ankur Patel 11467 views
- Polynomials by Divyanshu Saxena 6794 views

No Downloads

Total views

13,992

On SlideShare

0

From Embeds

0

Number of Embeds

15

Shares

0

Downloads

1,283

Comments

0

Likes

35

No embeds

No notes for slide

- 1. In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative, whole- number exponents. Polynomials appear in a wide variety of areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions.
- 2. Let x be a variable n, be a positive integer and as, a1,a2,….an be constants (real nos.) Then, f(x) = anxn+ an-1xn-1+….+a1x+xo anxn,an-1xn-1,….a1x and ao are known as the terms of the polynomial. an,an-1,an-2,….a1 and ao are their coefficients. For example: • p(x) = 3x – 2 is a polynomial in variable x. • q(x) = 3y2 – 2y + 4 is a polynomial in variable y. • f(u) = 1/2u3 – 3u2 + 2u – 4 is a polynomial in variable u.
- 3. •A polynomial of degree 1 is called a Linear Polynomial. Its general form is ax+b where a is not equal to 0 •A polynomial of degree 2 is called a Quadratic Polynomial. Its general form is ax3+bx2+cx, where a is not equal to zero •A polynomial of degree 3 is called a Cubic Polynomial. Its general form is ax3+bx2+cx+d, where a is not equal to zero. •A polynomial of degree zero is called a Constant Polynomial
- 4. LINEAR POLYNOMIAL For example: p(x) = 4x – 3, q(x) = 3y are linear polynomials. Any linear polynomial is in the form ax + b, where a, b are real nos. and a ≠ 0. QUADRATIC POLYNOMIAL For example: f(x) = √3x2 – 4/3x + ½, q(w) = 2/3w2 + 4 are quadratic polynomials with real coefficients.
- 5. For example: If(x) = 7, g(x) = -3/2, h(x) = 2 are constant polynomials. CUBIC POLYNOMIAL CONSTANT POLYNOMIAL For example: f(x) = 9/5x3 – 2x2 + 7/3x _1/5 is a cubic polynomial in variable x.
- 6. If f(x) is a polynomial and y is any real no. then real no. obtained by replacing x by y in f(x) is called the value of f(x) at x = y and is denoted by f(x). VALUE OF POLYNOMIAL ZEROES OF POLYNOMIAL A real no. x is a zero of the polynomial f(x),is f(x) = 0 Finding a zero of the polynomial means solving polynomial equation f(x) = 0.
- 7. 1. f(x) = 3 CONSTANT FUNCTION DEGREE = 0 MAX. ZEROES = 0
- 8. 2. f(x) = x + 2 LINEAR FUNCTION DEGREE =1 MAX. ZEROES = 1
- 9. 3. f(x) = x2 + 3x + 2 QUADRATIC FUNCTION DEGREE = 2 MAX. ZEROES = 2 These curves are also called as parabolas
- 10. 4. f(x) = x3 + 4x2 + 2 CUBIC FUNCTION DEGREE = 3 MAX. ZEROES = 3
- 11. α + β = - coefficient of x Coefficient of x2 = - b a αβ = constant term Coefficient of x2 = c a
- 12. α + β + γ = -Coefficient of x2 = -b Coefficient of x3 a αβ + βγ + γα = Coefficient of x = c Coefficient of x3 a αβγ = - Constant term = d Coefficient of x3 a
- 13. DIVISION ALGORITHM
- 14. •If f(x) and g(x) are any two polynomials with g(x) ≠ 0,then we can always find polynomials q(x), and r(x) such that : F(x) = q(x) g(x) + r(x), Where r(x) = 0 or degree r(x) < degree g(x) •ON VERYFYING THE DIVISION ALGORITHM FOR POLYNOMIALS. •ON FINDING THE QUOTIENT AND REMAINDER USING DIVISION ALGORITHM. •ON CHECKING WHETHER A GIVEN POLYNOMIAL IS A FACTOR OF THE OTHER POLYNIMIAL BY APPLYING THEDIVISION ALGORITHM •ON FINDING THE REMAINING ZEROES OF A POLYNOMIAL WHEN SOME OF ITS ZEROES ARE GIVEN.

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment