Upcoming SlideShare
×

# MB1002 QR

799 views

Published on

2 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

Views
Total views
799
On SlideShare
0
From Embeds
0
Number of Embeds
7
Actions
Shares
0
33
0
Likes
2
Embeds 0
No embeds

No notes for slide

### MB1002 QR

1. 1. In this document you can review important • Definitions • Facts • Formulae • Procedures Class – X, CBSE MB1002: Polynomials Learn Math for Free. Visit www.ganitgurooz.com
2. 2. What is a linear polynomial? Class – X,CBSE MB1002: Polynomials Important Definitions Topic: Linear Polynomial Learn Math for Free. Visit www.ganitgurooz.com
3. 3. What is a linear polynomial? Class – X,CBSE MB1002: Polynomials Important Definitions Topic: Linear Polynomial Learn Math for Free. Visit www.ganitgurooz.com A polynomial of degree one is called a linear polynomial.
4. 4. What is a quadratic polynomial? Class – X,CBSE MB1002: Polynomials Important Definitions Topic: Quadratic Polynomial Learn Math for Free. Visit www.ganitgurooz.com
5. 5. What is a quadratic polynomial? Class – X,CBSE MB1002: Polynomials Important Definitions Topic: Quadratic Polynomial Learn Math for Free. Visit www.ganitgurooz.com A polynomial of degree two is called a quadratic polynomial.
6. 6. How do a quadratic polynomial is represented in terms of x? Class – X,CBSE MB1002: Polynomials Important Definitions Topic: Quadratic Polynomial Learn Math for Free. Visit www.ganitgurooz.com
7. 7. How do a quadratic polynomial is represented in terms of x? Class – X,CBSE MB1002: Polynomials Important Definitions Topic: Quadratic Polynomial Learn Math for Free. Visit www.ganitgurooz.com 2 A quadratic polynomial in with real coefficients is of the form , where , , are real number with 0. x ax bx c a b c a
8. 8. What is a cubic polynomial? Class – X,CBSE MB1002: Polynomials Important Definitions Topic: Cubic Polynomial Learn Math for Free. Visit www.ganitgurooz.com
9. 9. What is a cubic polynomial? Class – X,CBSE MB1002: Polynomials Important Definitions Topic: Cubic Polynomial Learn Math for Free. Visit www.ganitgurooz.com A polynomial of degree three is called a cubic polynomial.
10. 10. Class – X,CBSE MB1002: Polynomials Important Definitions Topic: Zero of a Polynomial Learn Math for Free. Visit www.ganitgurooz.com What is a zero of a polynomial ( )?p x
11. 11. Class – X,CBSE MB1002: Polynomials Important Definitions Topic: Zero of a Polynomial Learn Math for Free. Visit www.ganitgurooz.com A real number ' ' is a zero of a polynomial if 0. In this case, is also called root of the equation =0. a p x p a a a p x What is a zero of a polynomial ( )?p x
12. 12. Fact # 1 Every linear polynomial in one variable has a unique zero, a non- zero constant polynomial has no zero, and every real number is a zero of the zero polynomial. Class – X,CBSE MB1002: Polynomials Important Facts Topic: Linear Polynomial Learn Math for Free. Visit www.ganitgurooz.com
13. 13. The zeroes of a polynomial are precisely the x-coordinates of the points, where the graph of intersects the x-axis. Class – X,CBSE MB1002: Polynomials Important Facts Topic: Zero of a Polynomial Learn Math for Free. Visit www.ganitgurooz.com Fact # 2
14. 14. Class – X,CBSE MB1002: Polynomials Important Facts Topic: Quadratic Polynomial Learn Math for Free. Visit www.ganitgurooz.com Fact # 3 A quadratic polynomial can have at most 2 zeroes.
15. 15. Class – X,CBSE MB1002: Polynomials Important Facts Topic: Cubic Polynomial Learn Math for Free. Visit www.ganitgurooz.com Fact # 4 A cubic polynomial can have at most 3 zeroes.
16. 16. The division algorithm states that given any polynomial and any non-zero polynomial, there are polynomials and such that Class – X,CBSE MB1002: Polynomials Important Facts Topic: Division Algorithm for Polynomials Learn Math for Free. Visit www.ganitgurooz.com p x g x q x r x ,where 0 or degree of degree g .p x g x q x r x r x r x x Fact # 5
17. 17. Class – X,CBSE MB1002: Polynomials Important Formulae Topic: Quadratic Polynomial 2 If and are the zeroes of the quadratic polynomial ,thenax bx c + , . b c a a Learn Math for Free. Visit www.ganitgurooz.com
18. 18. Class – X,CBSE MB1002: Polynomials Important Formulae Topic: Cubic Polynomial If , , Learn Math for Free. Visit www.ganitgurooz.com 3 2 0,thenax bx cx d , and . b a c a a d a are the zeroes of the cubic polynomial
19. 19. How to find the number of zeroes of a polynomial from its graph. Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Zeroes of a Polynomial Learn Math for Free. Visit www.ganitgurooz.com p x
20. 20. How to find the number of zeroes of a polynomial from its graph? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Zeroes of a Polynomial Learn Math for Free. Visit www.ganitgurooz.com : Imagine that the graph is being extended on both sides to infinity.Step1 p x
21. 21. How to find the number of zeroes of a polynomial from its graph? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Zeroes of a Polynomial Learn Math for Free. Visit www.ganitgurooz.com : Imagine that the graph is being extended on both sides to infinity. : Determine the number of points where the graph intersects (or touches) the x-axis. Step1 Step2 p x
22. 22. How to find the number of zeroes of a polynomial from its graph? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Zeroes of a Polynomial Learn Math for Free. Visit www.ganitgurooz.com : Imagine that the graph is being extended on both sides to infinity. : Determine the number of points where the graph intersects (or touches) the x-axis. : This is the number of real zeros Step1 Step2 Step3 of the polynomial. p x
23. 23. How to determine the zeroes of the polynomials ? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Zeroes of a Polynomial Learn Math for Free. Visit www.ganitgurooz.com p x
24. 24. How to determine the zeroes of the polynomials ? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Zeroes of a Polynomial Learn Math for Free. Visit www.ganitgurooz.com : Put 0.p xStep1 p x
25. 25. How to determine the zeroes of the polynomials ? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Zeroes of a Polynomial Learn Math for Free. Visit www.ganitgurooz.com : Put 0. : Factorise into linear factors. p x p x Step1 Step2 p x
26. 26. How to determine the zeroes of the polynomials ? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Zeroes of a Polynomial Learn Math for Free. Visit www.ganitgurooz.com : Put 0. : Factorise into linear factors. : Put each linear factor equal to 0. p x p x Step1 Step2 Step3 p x
27. 27. How to determine the zeroes of the polynomials ? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Zeroes of a Polynomial Learn Math for Free. Visit www.ganitgurooz.com : Put 0. : Factorise into linear factors. : Put each linear factor equal to 0. : Solve each linear equation obtained in step 3 to find zeros of the polynomial . p x p x p x Step1 Step2 Step3 Step4 p x
28. 28. How to form the quadratic polynomial given the sum and product of its zeroes? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Quadratic Polynomial Learn Math for Free. Visit www.ganitgurooz.com p x
29. 29. How to form the quadratic polynomial given the sum and product of its zeroes? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Quadratic Polynomial Learn Math for Free. Visit www.ganitgurooz.com p x : Suppose that the zeros of the are and .p xStep1
30. 30. How to form the quadratic polynomial given the sum and product of its zeroes? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Quadratic Polynomial Learn Math for Free. Visit www.ganitgurooz.com p x : Suppose that the zeros of the are and . : Let S and P be the sum and product of these zeros. Thus, and . p x S P Step1 Step2
31. 31. How to form the quadratic polynomial given the sum and product of its zeroes? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Quadratic Polynomial Learn Math for Free. Visit www.ganitgurooz.com p x : Suppose that the zeros of the are and . : Let S and P be the sum and product of these zeros. Thus, and . : Let the coefficients of the polynomial be , , and c. p x S P p x a b Step1 Step2 Step3
32. 32. How to form the quadratic polynomial given the sum and product of its zeroes? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Quadratic Polynomial Learn Math for Free. Visit www.ganitgurooz.com p x : Suppose that the zeros of the are and . : Let S and P be the sum and product of these zeros. Thus, and . : Let the coefficients of the polynomial be , , and c. p x S P p x a b Step1 Step2 Step3 Step : Then we get, , . b S a c P a 4
33. 33. How to form the quadratic polynomial given the sum and product of its zeroes? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Quadratic Polynomial Learn Math for Free. Visit www.ganitgurooz.com p x : Suppose that the zeros of the are and . : Let S and P be the sum and product of these zeros. Thus, and . : Let the coefficients of the polynomial be , , and . p x S P p x a b c Step1 Step2 Step3
34. 34. How to form the quadratic polynomial given the sum and product of its zeroes? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Quadratic Polynomial Learn Math for Free. Visit www.ganitgurooz.com p x : Solve these equations simultaneously to determine the values of , , and .a b cStep5 : Then we get, , . b S a c P a Step4
35. 35. How to divide two polynomials to find the remainder and quotient? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Division Algorithm for Polynomials Learn Math for Free. Visit www.ganitgurooz.com
36. 36. How to divide two polynomials to find the remainder and quotient? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Division Algorithm for Polynomials Learn Math for Free. Visit www.ganitgurooz.com : Find the degree of the dividend and degree of divisor.Step1
37. 37. How to divide two polynomials to find the remainder and quotient? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Division Algorithm for Polynomials Learn Math for Free. Visit www.ganitgurooz.com : Find the degree of the dividend and degree of divisor. : Check that degree of dividend degree of divisor. If not, we cannot divide. Step1 Step2
38. 38. How to divide two polynomials to find the remainder and quotient? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Division Algorithm for Polynomials Learn Math for Free. Visit www.ganitgurooz.com : Find the degree of the dividend and degree of divisor. : Check that degree of dividend > degree of divisor. If not, we cannot divide. : Divide the first term of the dividend by the Step1 Step2 Step3 first term of the divisor to get the first term of the quotient.
39. 39. How to divide two polynomials to find the remainder and quotient? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Division Algorithm for Polynomials Learn Math for Free. Visit www.ganitgurooz.com : Find the degree of the dividend and degree of divisor. : Check that degree of dividend > degree of divisor. If not, we cannot divide. : Divide the first term of the dividend by the Step1 Step2 Step3 first term of the divisor to get the first term of the quotient. : Multiply the divisor by the first term of the quotient and subtract it from the dividend.Step4
40. 40. How to divide two polynomials to find the remainder and quotient? Class – X,CBSE MB1002: Polynomials Important Procedures Topic: Division Algorithm for Polynomials Learn Math for Free. Visit www.ganitgurooz.com : Find the degree of the dividend and degree of divisor. : Check that degree of dividend > degree of divisor. If not, we cannot divide. : Divide the first term of the dividend by the Step1 Step2 Step3 first term of the divisor to get the first term of the quotient. : Multiply the divisor by the first term of the quotient and subtract it from the dividend. : Repeat steps 2 4 t Step4 Step5 aking the different found in step 4 as the new dividend.