Topic:- Polynomials Subtopic: Geometrical Meaning of the Zeroes of a Polynomial Class:- X Time required:-One period (35 – 40 minute)

Lesson objectives:- General Objectives:- To develop the logical reasoning of the students. Specific objectives:- After the lesson students will be able to Learn what the geometrical meaning of zeroes of a polynomial is. Deduce that how many (at most) zeroes a polynomial can have. Material needed: Graph papers, computer, graphical calculator, OHP.

Expected previous skills:- Previous Knowledge test minutes Motivation (Introduction of the topic)--- 3 minutes. Group activity minutes Discussion/ presentation minutes Individual Evaluation:-8-10 minutes. Home assignment minutes The students are expected to plot points on graph whose co-ordinates are given. Time management:-

Lesson launch:- Previous Knowledge test:- take about 2 minutes to recapitulate what has been studied in previous lessons. Ask the students some questions such as What do you mean by polynomial? What do you understand by degree of a polynomial? What do you mean by ‘zero’ of a polynomial? What is the co-efficient of x and the constant term in the polynomial ‘3x+5’ What is the co-efficient of x and the constant term in the polynomial ‘ax+b’

Motivation (Introduction of the topic):- We have studied that what is a polynomial and how to find the zeroes of a polynomial. If ‘k’ is a zero of p(x) = ax+b, a 0, then p(k) = 0 i.e. ak + b = 0 i.e. k = -b/a So, the zero of linear polynomial ax+b, a 0 is –b/a = Thus we see that zero of a linear polynomial is related to its coefficients. Here we will see that why the zeroes of polynomial are so important. we shall discuss the graphical representation of polynomials of degree 1, 2 and 3, and try to understand the geometrical meaning of zeroes of the polynomial. Let us discuss about linear polynomial today.

Worksheet Expression Is it a polyno mial or not If yes, degree of polynomial Linear or not Corresponding polynomial equation Co-ordinate of the point where graph cuts x-axis (from graph Zero of the polynomial Whether zero of polynomial is equal to x- coordinate of point where graph cuts x-axis X + 7 x 5

Act in Groups:- Divide the class into small groups of 3-4 students each and provide each group with a graph paper. Assign each group with following task: Plot the graph of a linear polynomial equation Group 1 will plot y = 2x +8, Group 2 will plot y = 3x + 12, Group 3 will plot y = x + 7, Group 4 will plot y = -5x + 10 and so on. Find the point where the graph intersects x-axis. Also find the zero of the polynomial using the relation {Zero of linear polynomial ax+b, a 0 = –b/a = } Allow the students complete the task within 5-6 minutes. Leader of each group shall discuss their findings with the class turn by turn. Teacher captures the points of explanation of each group on the blackboard.

Post activity Discussion Note:- A “word Bank” may be created either with every chapter or separately and the difficult words, terms alongwith their meaning and translation( Hindi to English)should be recorded. It would be of great help especially for Hindi medium students.

Teacher(as mentor)- student dialogueWord-Bank Mentor (M):- Can you see, is there any relation between the zero of polynomial and the point where the graph intersects the X-axis? S:- yes, zero of the polynomial is equal to the X-coordinate of the point where the graph intersects the X-axis. M:-Yes, good. The teacher may explain with one or more examples (from the worksheet) to make this point clear and generalise the conclusion as follows. M:- In general for a linear polynomial p(x) = ax+b, a 0, the graph of y = ax+b is a straight line which intersects the X-axis at exactly one point namely (-b/a,0). Therefore linear polynomial p(x) = ax+b, a 0 has exactly one zero namely X-coordinate of the point where the graph of y = ax+b intersect X-axis. Polynomial Zero of polynomial Co-ordinate Linear intersect

Individual Evaluation:- To evaluate the individual achievement of the students following type of a worksheet is suggested.worksheet

Home Assignment:- consider the following problem: 1. Length of a room is 3 meter more than the twice of its breadth. Considering the breadth as a variable, say x, express the length of the room as polynomial in terms of ‘x’ (breadth) and answer the following questions: What type of polynomial do you get? What is the degree of this polynomial? Plot the graph of corresponding polynomial equation. How many zeroes this polynomial have? Also find the zeroes. Verify that the zero of the polynomial is equal to the x-coordinate of the point where the graph intersects x-axis.

2. Age of father is 5years less than the 4 times the age of the child. Considering the age of the child as a variable ‘t’, express father’s age in terms of age of the child. and answer the following questions: What type of polynomial do you get? What is the degree of this polynomial? Plot the graph of corresponding polynomial equation. How many zeroes these polynomials have? Also find the zeroes. Verify that the zero of the polynomial is equal to the x- coordinate of the point where the graph intersects x- axis.

Above lesson plan is in a form of draft, any further amendments or suggestion are always cordially accepted. Sh Pawan Kumar, Lect. Maths,GSSS Sihunta, Distt Chamba. Sh Bhim Singh, Lect. Maths,GSSS Drang, Distt. Mandi. Sh Dheeraj Vyas, Lect. Maths, GSSS khalet, Distt Kangra. Sh Om Prakash, T.G.T. (N/M,), GSSS Chandi, Distt Solan. Sh. Satya Prakash Sharma Lect. Maths GSSS Dehar Distt. Mandi. Sh. Kamal Kishore Lect. Maths GSSS Mahadev Distt. Mandi. Sh. Surender Chauhan Lect. Maths GSSS Portmore Distt. Shimla. Sh. Roop Singh Lect. Maths GSSS Randhara Distt. Mandi Sh. Lalit Kumar Lect. Maths GSSS Nagwain Distt. Mandi. Sh. Bhagat Singh Lect. Maths GSSS Tangling Distt. Kinnaur. Sh. Yog Raj Lect. Maths GSSS Baryara Distt. Mandi i