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CBSE Worksheet for chapter-2 Polynomial class 10

Worksheet For class 10

Find CBSE Worksheet for chapter- 2 Polynomial class 10

CLASS-10

BOARD: CBSE

Mathematic Worksheet - 2

TOPIC: Polynomial

For other CBSE Worksheet for class 10 Mathematic check out main page of Entrancei. 

SUMMARY

An algebraic expression f(x) of the form f(x)= a0 + a1x +a2x2+…….+an xn ,where a0,a1, a2……. an are real numbers and all the index of x are non negative integers is called polynomial in x and the highest index n is called as the degree of polynomial.

IMPORTANT FORMULAE

(x+a)2 =x2 +2ax+a2

(x-a)2 =x2 – 2ax +a2

x2-a2 =(x+a) (x-a)

x3+a3=(x+a) (x2-ax+a2)=(x+a)3 –3xa(x+a)

x3-a3=(x-a) (x2+ax+a2)=(x+a)3 +3xa(x-a)

(a + b + c) 2=a2+b2+c2+2ab+2bc+2ac

(a + b) 3= a3+b3+3ab (a + b)

(a-b) 3= a3-b3-3ab (a-b)

a3+b3+c3-3abc = (a +b +c) (a2+b2+c2-ab-bc-ca)

SPECIAL CASE : If a+ b +c=0 then a3+b3+c3=3abc

ZEROS OR ROOTS OF A POLYNOMIAL

A real number ‘a’ is a zero of a polynomial f(x),if f(a)=0.Here ‘a’ is called a root of the equation f(x) = 0

FACTOR THEOREM

Let p(x) be a polynomial of degree greater than or equal to ‘a’, be a real number such that p(a)=0,then (x-a) is a factor of p(x),then p(a)=0.

REMAINDER THEOREM

Let p(x) be any polynomial of degree greater than or equal to one and ‘a’ be any real number. If p(x)is a dividend by (x-a),then remainder is equal to p(a).let q(x) be the quotient and r(x) be the remainder when p(x) is divided by (x-a),then

Dividend=Divisor x Quotient + Remainder

OBJECTIVE

1) If 4x4-3x3-3x2+x+7 is divided by 1-2x then remainder will be:

a)57/8

b) (-59)/8

c) 55/8

d) (-55)/8

2) A quadratic polynomial is exactly divisible by(x+1) and (x+2) and leaves the remainder 4 after division by (x+3) then that polynomial is:

a) x2+6x+4

b) 2x2+6x+4

c) 2x2+6x-4

d) x2+6x-4

3) Graph of a quadratic equation is always;

a) straight line

b) circle

c) parabola

d) hyperbola

4) The graph of a polynomial y=x3-x2+x is always passing through the point

a) (0,0)

b) (3,2)

c) (1,-2)

d) all of these

5) Which of the following touches X-axis?

a) x2-2x+4

b) 3x2-6x+1

c) 4x2-16x+9

d)25x2-20x+4

SUBJECTIVE

1) Find the zeros of quadratic polynomial p(x)=4x2+24x+36 and verify the relationship between the zeros and their coefficient.

2) Find the quadratic polynomial whose zeros are 3+ and 3-

3) On dividing x3-3x2-x-2 by a polynomial g(x), The quotient and remainder were x-2 and -2x+4 respectively. Find g(x).

4) α, β, ⅟ are zeros of cubic polynomial x3-12x2-44-c.If α ,β,⅟ are in A.P, find values of c.

5) What must be subtracted fromx4+2x3-13x2-12x+21 so that the result is exactly divisible by x2-4x+3

6) If α ,β are zero of quadratic polynomial kx2+4x+4,find the values of k such that (α + β)2 -2 αβ =24.

7) If α, β are zero of quadratic polynomial 2y2+7y+5,write the values of α + β+ αβ.

8) For what values of k, is 3 a zero of y the polynomial 2x2+x+k?

Answers

Objective:

1) b

2) b

3) c

4) a

5) d

6) a

Subjective:

1) 3,-3

2) k(x2-6x+4)

3) x2-x+1

4) c=-48

5) 2x-3

6) k= ,-1

7) -1

8) k=-21

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