POLYNOMIALS ( LECTURE 3)

1ST MAY
LESSON 3 POLYNOMIALS

GOOD MORNING!!

Guidelines for the class:

1. Note down  the work in your register on a regular basis.

2. Please feel free to ask, if you have any doubt by dropping a message in the comment box.

3. Make a column on the right hand side, if you need to do any rough work

4. Write  today's date.

5. Write the chapter number and name.

6. Text in red has to be noted down as its your class work.

 Relationship between Zeroes and Coefficients of a Polynomial

In the previous class you learnt how to find zeroes of a quadratic polynomial and verify the relation between zeroes and coefficients.

Today we will cover the following learning outcomes:(write down)
I will be able to:
1. recall what is sum and product of zeroes of a quadratic polynomial.
2.. Form a quadratic polynomial when sum and product of zeroes are given.
. 





LET'S REVISE WHAT IS sum and product of  ZEROES  OF A POLYNOMIAL

1.Find the sum and product of the zeros of the following polynomial:
x2−5x+6  

2.

Find the sum and product of the zeros of the following polynomial:

4x2+15x+11

CHECK YOUR ANSWERS
1) 5, 6

EXPLAINATION: SUM OF ZEROES = --b/a, product of zeroes =c/a

where a is coefficient of x², b  is coefficient of x, c is constant
2) -15/4, 11/4

EXPLAINATION: SUM OF ZEROES = --b/a, product of zeroes =c/a

where a is coefficient of x², b  is coefficient of x, c is constant

REMEMBER DOING IT IN THE PREVIOUS CLASS !!

Now, we will see how to form a quadratic polynomial if sum and product of zeroes are given

look at the eg.☟

Now, note down the eg you just saw in the video

eg Find a quadratic polynomial, the sum and product of whose zeroes are –3 and 2, respectively.

 Solution : Let the quadratic polynomial be ax² + bx + c, and its zeroes be α and β.
 We have

sum of zeroes   =-3(given)

so, α + β = – 3 =  b /a  ,

Product of zeroes = 2(given)

and αβ = 2 = c /a

.comparing we get

 a = 1, then b = 3 and c = 2. 

So, one quadratic polynomial which fits the given conditions is
 x² + 3x + 2.

there is one more way you can find the polynomial


the required polynomial is of the form  :
  k(x² -(sum of zeroes) + product of zeroes)


where k is any real number.

so, as you keep changing the values of 'k' you can find different polynomials having same sum and product of zeroes.

In the previous eg we discussed about polynomial when sum and product of zeroes are integers.

But it will not be always like that!!

Look at the other case(q2(i)of EX 2.2) ☟

Let's do EX 2.2 Q2



Q2Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively

(I)  (you saw it in the video above)

Let quadratic polynomial be 

Let α and β are two zeroes of above quadratic polynomial.

α+β =  = 

α × β = -1   = 

 Quadratic polynomial which satisfies above conditions = 

(ii) √2  ,1/3
  

Let α and β be two zeros of above quadratic polynomial.

α+β = = 

α × β =  which is equal to 

 

 Quadratic polynomial which satisfies above conditions = 3x² -3√2 x + 1

(iii) 0, 

Let quadratic polynomial be 

Let α and β be two zeros of above quadratic polynomial.

α+β = 0  = 

α  β =  = 

 

 Quadratic polynomial which satisfies above conditions 

Now, you can complete parts iv ,v, vi as HW

QUESTIONS FOR HW

WE FINISH OUR CLASS HERE!
SEE YOU TOMORROW!
KEEP SAFE!!