POLYNOMIALS ( LECTURE 2)

lesson 2   polynomials



 LETS  RECALL THE TERM  FACTORISATION WHICH WE HAVE LEARNT IN  CLASS  9 AND RECALL ,HOW TO  FACTORISE   A QUADRATIC POLYNOMIAL

. Methods   1.   using   Idetities  

or   2.   splitting the middle term
NOTE :-
 1. Its a video of  30 mins duration with many examples  explaining  how to factorise the  polynomial by splitting the middle term method .

2.Watch 1 or 2 examples ( 7 mins  ).

3.Can practice  all the sums later( if needed.)

 4.CLICK THE GIVEN LINK FOR  FACTORISATION OF QUADRATIC POLYNOMIAL
LINK


 LETS TAKE AN  EXAMPLE  ( TO  FACTORISE)  
Example 1 : 4x2 + 12x + 5
Solution: We have to find two numbers, whose
sum is 12 (middle term) and when
multiplied (first and last term) i.e. 4 X 5 we get 20

So these two numbers are -
10 + 2 = 12
10 X 2 = 20

Now we put both 10 and 2 numbers in the middle term of 12x and we get

∴ 4x2 + 12x + 5
 = 4x2 + 10x + 2x + 5
or 2x(2x + 5) + 1(2x + 5)
or (2x + 5)(2x + 1)

Try       4x2 + 8x - 5  (CW)         Ans ((2x + 5)(2x - 1)

TODAYS LEARNING OUTCOMES  
i will be able to  find the zeroes of a quadratic polynomial and verify the relationship between  zeroes and the coefficients . 

Read the  Question given below👇 

Write the zeroes of the polynomial x2 + 2x + 1.

Did u notice the word   zeroes   ( To be written👇)


 what is   zero  of a polynomial ?

Zero of a polynomial is  the real value of the variable for which the value of the polynomial becomes zero. . 
. example   k is  said to be zero of a polynomial p(x)   if p(k) = 0
    lets take a linear  polynomial    p(x)=    x - 1   ,
what value of ' x'.  will make the value of  polynomial  as zero
   if we take x= 1,then the value of polynomial becomes     p(1) = 1-1 = 0
Therefore  x=1 is the zero of the given polynomial  p(x)

what are  zeroes of a polynomial ?

Zeroes are  a plural form of zero .Zeroes of a polynomial  are the real values of the variable for which the value of the polynomial becomes zero.
 ,so

linear  polynomial   degree 1 ( highest power of variable = 1)     number of zero = 1
quadratic polynomial  degree 2( highest power of variable =  2)   number of zeroes = 2
cubic polynomial   degree 3 ( highest power of variable = 3)     number of zeroes  = 3

Now you have understood .Lets try to find the zeroes of the  given question 👇  (in register)

 Write the zeroes of the polynomial x2 + 2x + 1.

The Answer is 

The value of x which will make the value of the given polynomial p(x) as zero

Let  p(x) = 0
   ⇒   x2 + 2x + 1=0
  ⇒    x2 + 1x +1x + 1=0.  
⇒  x(x +1) + 1(x + 1)=0
 ⇒    (x +1) (x+1)=0
therefore     x+1=0  , which gives x = -1
or other factor  x+1 = 0, which also gives x = -1

The zeroes of p(x) = x2 + 2x + 1=0 are -1 and -1 
𝝰 = -1  and 𝛃= -1 

 NOTE : -These two zeroes are denoted by 𝝰  and 𝛃
standard form of a quadratic poly. is   ax2 + bx + c,where a,b and c are real numbers.

To know more about it click the given link

TO UNDERSTAND THE RELATION OF ZEROES TO ITS COEFFICIENTS OF A POLYNOMIAL,click the link given below
                                           LINK
write   in your register 👇

•  Relationship between the zeroes and the coefficients of a Polynomial.

     (i)   If α, β are zeroes / roots of p(x) = a x2 + bx + c, then

              

E


,LETS try to understand by solving Q1 (ii) of   Ex  2.2 

Lets solve Q1 (iv) (HINT   4u2 + 8u = 4u ( u + 2)   

 =                                      and u +2 = 0 
       find  𝝰   and 𝛃 and verify.  (cw)

Q1 (v)

(HW)  Ex  6.2   Q1 ( i, iii and vi)


Q2  Find the zeroes of the quadratic polynomial x2 + 5x + 6 and verify the relationship between the zeroes and the coefficients.

              Thanks   SEE YOU TOMORROW AND  TAKE CARE OF YOUR SELF 😊