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- 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. What is a linear polynomial? Class – X,CBSE MB1002: Polynomials Important Definitions Topic: Linear Polynomial Learn Math for Free. Visit www.ganitgurooz.com
- 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. What is a quadratic polynomial? Class – X,CBSE MB1002: Polynomials Important Definitions Topic: Quadratic Polynomial Learn Math for Free. Visit www.ganitgurooz.com
- 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. 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. 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. What is a cubic polynomial? Class – X,CBSE MB1002: Polynomials Important Definitions Topic: Cubic Polynomial Learn Math for Free. Visit www.ganitgurooz.com
- 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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.

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