CBSE Worksheet for chapter-2 Polynomial class 10
Worksheet For class 10
An algebraic expression f(x) of the form f(x)= a0x2+…….+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.
- (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
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.
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
Q1. If 4x4-3x3-3x2+x+7 is divided by 1-2x then remainder will be:
Q2. 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:
- x2 + 6x + 4
- 2x2 + 6x + 4
- 2x2 + 6x - 4
- x2 + 6x - 4
Q3. Graph of a quadratic equation is always;
- straight line
Q4. The graph of a polynomial y = x3 - x2 + x is always passing through the point
- all of these
Q5. Which of the following touches X-axis?
- x2 - 2x + 4
- 3x2 - 6x + 1
- 4x2 - 16x + 9
- 25x2 - 20x + 4
Q1. Find the zeros of quadratic polynomial p(x) = 4x2 + 24x + 36 and verify the relationship between the zeros and their coefficient.
Q2. Find the quadratic polynomial whose zeros are 3+ and 3-
Q3. 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).
Q4. α, β, ⅟ are zeros of cubic polynomial x3-12x2- 44 - c.If α ,β,⅟ are in A.P, find values of c.
Q5. What must be subtracted fromx4 + 2x3 - 13x2 - 12x + 21 so that the result is exactly divisible by x2 - 4x + 3
Q6. If α ,β are zero of quadratic polynomial kx2 + 4x + 4,find the values of k such that (α + β)2 -2 αβ =24.
Q7. If α, β are zero of quadratic polynomial 2y2 + 7y + 5,write the values of α + β+ αβ.
Q8. For what values of k, is 3 a zero of y the polynomial 2x2 + x + k?
Q2. k(x2 - 6x + 4)
Q3. x2 - x + 1
Q4.c = - 48
Q5.2x - 3
Q6. k = -1
Q8. k = - 21
- Class 10 Physics Notes
- Class 10 Chemistry Notes
- Class 10 Biology Notes
- Class 10 Maths Notes
- Chapter Wise Quiz Class 10 Physics
- Chapter Wise Quiz Class 10 Chemistry
- Chapter Wise Quiz Class 10 Biology
- Chapter Wise Quiz Class 10 Maths
- Previous year Board Papers
- Sample Papers Maths Class 10
- Sample Papers Science Class 10
- NCERT Maths Solutions Class-10