Transcript 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.

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:The students are expected to plot points on graph whose
co-ordinates are given.
Time management:•Previous Knowledge test---- 5 minutes
•Motivation (Introduction of the topic)--- 3 minutes.
•Group activity
------ 8-10 minutes
•Discussion/ presentation----- 7-8 minuts
•Individual Evaluation:-8-10 minutes.
•Home assignment --------3-4 minutes
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.
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 alogwith 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 dialogue
Word-Bank
Mentor (M):- Can you see, is there any relation between the zero of polynomial 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 Xcoordinate of the point where the graph of y = ax+b intersect X-axis.
Zero of
polynomial
Co-ordinate
Linear
intersect
Individual Evaluation:To evaluate the individual achievement of the students following type
of a worksheet is suggested .
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
suggestions are always cordially accepted.
With thanks
•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