Math Magic Cl 9: POLYNOMIALS (LECTURE 3)

lesson 3 polynomials

LESSON 3 POLYNOMIALS

GOOD MORNING EVERYONE!!

Few Instructions

Text in red has to be noted down as its your class work.
Text in blue are videos (watch )

Text in green is your homework

AQAQ

The polynomial of type ax2 + bx + c, a = 0 is of type

(a) linear

(b) quadratic

(c) cubic

(d) Biquadratic

In the previous class we discussed about

1. CLASSIFY THE POLYNOMIALS ON THE BASIS OF NUMBER OF TERMS AND DEGREE.
2. COMPREHEND AND MEMORIZE ABOUT SOME SPECIAL POLYNOMIALS.

TODAY'S LEARNING OUTCOMES:
I WILL BE ABLE TO:

1. EVALUATE VALUE OF A POLYNOMIAL
2.EVALUATE ZERO OF A POLYNOMIAL.

Value of a Polynomial

For Example:
Find value of this polynomialp(x) = x + 2 at x =1

.(step i) Consider p(x) = x +1 .

,( step ii)   If we put x = 1 in p(x), we get

(step (iii) p(1) = 1 + 2 = 3

Thus,3 is the value of the polynomial p(x). at x = 1

Zero of a Polynomial : The value of variable for which the polynomial becomes zero is called as the zero of the polynomial
.
For Example:
Find zero of this polynomial  p(x) = x + 2.

(stepi)   p(x) = x + 2.

(stepii) If we put x = -2 in p(x), , we get

.(stepiii)  p(-2) = -2 + 2 = 0

Thus,( -2) is a zero of the polynomial p(x)................................ why?.

(NOTE :- The value of polynomial p(x) has become zero , when x=(_-2 ).

TO KNOW MORE ,CLICK THE LINK GIVEN BELOW

ZERO OF A POLYNOMIAL

Lets solve another Example: (Read carefully and try to understand )

Find value of polynomial 3a2 + 5a + 1 at a = 3

(i) Here, p(a) = 3a2 + 5a + 2.
(ii) Now, substituting a = 3, we get
,(iii) p(3) = 3 x (3)2 + 5 x 3 + 2 = 27 + 15 + 2 = 44

. Thus the value of polynomial p(x) is 44, if a = 3

Find zero of polynomial 3a2 + 5a + 1 .

(i) Here, p(a) = 3a2 + 5a + 2
.(ii) Now, substituting a = ( -1), we get,
(iii) p(-1 ) = 3 x (-1 )2 + 5 x (-1) + 2 = 3 - 5 + 2 = 0

. Thus the zero of polynomial p(x) is (-1)

so Answer these questions

The value of the polynomial p(x) = 2x + 5 is,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,( 5 or 7 ) , at x = 1,,

The value of p (x) = x + 2 is 2 , if the value of x is ..............................( one / zero)

The value of p (x) = x2 + 4x + 2 at x = ( -1) is ................. ( -1 or 7 )

see the video given for solving Q1 Ex 2.2 (cw)

Q1EX 2.2

solution:- 1 (iii) p(x)= 5x-4x2 + 3 at x=2

see the video given for solving Q3 Ex 2.2

Q3 EX. 2

Now lets solve Q3

CLICK THE LINK GIVEN BELOW

FINDING ZERO OF A LINEAR POLYNOMIAL

Now answer the following

The zero of the polynomial p(x) = 2x + 5 is,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,( 5/2 or -5./2 ),,

The number of zeros of x2 + 4x + 2 is...............................( one or two)

Q4 (i)

    Let's find the zero of given polynomial
   Q4 (vi)p(x) = ax , a ≠ 0

    since , p(x) = 0
   ⇒ ax = 0
  ⇒ x = 0   ,Thus zero of p(x) is 0

    (vii) p(x) = cx +d

  since , p(x) = 0
   ⇒ cx +d = 0
   ⇒ cx = -d
    ⇒ x = -d/c, Thus zero of p(x) is -d / c

NOTE -:

(i) A non-zero constant polynomial has no zero
.(ii) A linear polynomial has one and only one zero
.(iii) A zero of a polynomial might not be 0 or 0 might be a zero of a polynomial
.(iv) A polynomial can have more than one zero. (quadratic , cubic.......)