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Class 10 Maths Important Questions for Polynomials




Given below are the Class 10 Maths Important Questions for Polynomials
a) Concepts questions
b) Calculation problems
c) Multiple choice questions
d) Long answer questions
e) Fill in the blanks
f) Match the column

Match the column


A.
Degree of polynomial
Polynomial
1
x5 -3x2 +1
2
x-1
3
x4-3x2+2+ 3x3
4
x2 -2x-1
5
1-3x3
B.
type of polynomial
Polynomial
monomial
X3 -4x2 +1
binomial
x-1
trinomial
x4-3x2+2+ 3x3
No appropriate match
x2 -2
3x3
C.
P(x)=5x3 -3x2+7x+2
P(0)
P(1)
P(5)
P(-1)
P(-2)


Multiple choice Questions


Question 1 Find the remainder  when x4+x3-2x2+x+1 is divided by x-1
a.1
b.5
c.2
d. 3

Question 2 Which of these identities is not true?
Class 10 Maths Important Questions  for Polynomials

Question 3 True or False statement
  1. P(x) =x-1 and g(x) =x2-2x +1 .  p(x) is a factor of g(x)
  2. The factor of 3x2 –x-4 are  (x+1)(3x-4)
  3. Every linear polynomial has only one zero
  4. Every real number is the zero’s of zero polynomial
  5. A binomial may have degree 6
  6. 1,2 are the zeroes of x2-3x+2
  7. The degree of zero polynomial is not defined
  8.  Graph of polynomial (x2-1) meets the  x-axis at one point
  9. Graph of constant polynomial never meets x axis

Question 4Factorize following
  1. x2 +9x+18
  2. 3x3 –x2-3x+1
  3. x3-23x2+142x-120
  4. 1+8x3

Match the column


A)
Graph of polynomial
Number of Zeros
Class 10 Maths Important Questions  for Polynomials
  0
Class 10 Maths Important Questions  for Polynomials
  1
Class 10 Maths Important Questions  for Polynomials
2
Class 10 Maths Important Questions  for Polynomials
  3
Class 10 Maths Important Questions  for Polynomials
  4
Class 10 Maths Important Questions  for Polynomials
  5
Class 10 Maths Important Questions  for Polynomials
  6
Class 10 Maths Important Questions  for Polynomials
  7

B.
Graph of polynomial
Type of polynomial
Class 10 Maths Important Questions  for Polynomials
  Linear polynomial
Class 10 Maths Important Questions  for Polynomials
  Quadratic polynomial
Class 10 Maths Important Questions  for Polynomials
 
Cubic polynomial
Class 10 Maths Important Questions  for Polynomials
  Constant polynomial
Class 10 Maths Important Questions  for Polynomials
  Class 10 Maths Important Questions  for Polynomials
  Class 10 Maths Important Questions  for Polynomials
  Class 10 Maths Important Questions  for Polynomials

Multiple Choice Questions


Question 1 If a and b are the zeroes of the polynomial  x2-11x +30, Find the value of a3 + b3
a.134
b.412
c.256
d.341

Question 2 S(x) = px2+(p-2)x +2. If  2 is the zero of this polynomial,what is the value of p
a.-1
b.1/2
c. -1/2
d. +1

Question 3if the zeroes of the quadratic equation are 11 and 2 ,what is expression for quadratic
a. x2-13x+22
b. x2-11x+22
c. x2-13x-22
d. x2+13x-22

Question 4 p(x) = x4 -6x3 +16x2 -25x +10
     q(x) = x2-2x+k
It is given
p(x) = r(x) q(x) + (x+a)
Find the value of k and a
a.2,-2
b. 5 ,-5
c. 7,3
d. 3,-1

Question 5 A cubic polynomial is given below
  S(x) =x3 -3x2+x+1
The zeroes of the polynomial are given as (p-q) ,p  and (p+q). What is the value p and q
a. p=1,q=√2 or -√2
b. p=1,q=2 or -2
c. p=1,q=1 or -1
d. None of these

Division of polynomial


s(x) =r(x) s(x) + w(x)
Find the value of r(x) and w(x) in each case
a. p(x) =x4+x3+2x2+3x+4
     s(x) =x+2
b. p(x) =x4+4
  s(x)=x2+x+1

More Practice Questions

Question 1. If the polynomial f(x) = x4 -6x3 + 16x2 – 25x + 10 is divided by another polynomial x2 -2x + k, the remainder comes out to be x + a, find k and a.

Question 2. Find all the zeroes of the polynomial x4 – 3x3 + 6x – 4, if two of its zeroes are √2  and -√2
Question 3. If p and q are he zeroes of the quadratic polynomial f(x) = x2 – 2x + 3, find a polynomial whose roots are:
  1. p + 2, q + 2
  2. (p-1)/(p+1) , (q-1)/(q+1)
Question 4. For what value of k, -7 is the zero of the polynomial 2x2 + 11x + (6k – 3)? Also find the other zero of the polynomial
Question 5. What must be added to f(x) = 4x4 + 2x3 – 2x2 + x – 1 so that the resulting polynomial is divisible by g(x) = x2 + 2x -3?
Question 6. Find k so that x2 + 2x + k is a factor of 2x4 + x3 – 14 x2 + 5x + 6. Also find all the zeroes of the two polynomials.
Question 7. If the zeroes of the quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then
(A) c and a have opposite signs
(B) c and b have opposite signs
(C) c and a have the same sign
(D) c and b have the same sign

Question 8. Find the zeroes of 2x3 – 11x2 + 17x – 6.
Question 9. If (x - 2) and [x – ½ ] are the factors of the polynomials qx2 + 5x + r prove that q = r

Question 10. Find k so that the polynomial x2 + 2x + k is a factor of polynomial 2x4 + x3 – 14x2 + 5x + 6. Also, find all the zeroes of the two polynomials.

Question 11. On dividing p(x) = x3 – 3x2 + x + 2 by a polynomial q(x), the quotient and remainder were x – 2 and -2x + 4, respectively. Find g(x).
Question 12. a, b, c are zeroes of cubic polynomial x3 – 2x2 + qx – r. If a + b = 0 then show that 2q = r.
Question 13. Find the remainder when x51 +51 is divided by (x+1).
Question 14. a,b and c are zeroes of polynomial x3 + px2 + qx + 2 such that a b + 1 = 0. Find the value of 2p + q + 5.

Question 15. Find the quadratic polynomial, the sum and product of whose zeroes are 4 and 1, respectively


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Reference Books for class 10

Given below are the links of some of the reference books for class 10 math.

  1. Oswaal CBSE Question Bank Class 10 Hindi B, English Communication Science, Social Science & Maths (Set of 5 Books)
  2. Mathematics for Class 10 by R D Sharma
  3. Pearson IIT Foundation Maths Class 10
  4. Secondary School Mathematics for Class 10
  5. Xam Idea Complete Course Mathematics Class 10

You can use above books for extra knowledge and practicing different questions.


Class 10 Maths Class 10 Science

Practice Question

Question 1 What is $1 - \sqrt {3}$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20






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