2 . Polynomials

SEBA Class 10 Maths Chapter 2 Polynomials

Chapter 2 . Polynomials

Class 10 Maths Chapter 2 Polynomials Multiple Choice Questions and Solutions :

Question: If 3 is a zero of the quadratic polynomial , then the value of is : [SEBA 2013]

(a) – 5 (b) 6 (c) 5 (d) 4

Solution : (B) – 10

[ Let ;

]

Question : If , then the value of is : [SEBA 2014]

(a) – 38 (b) – 39 (c) – 37 (d) – 36

Solution : (b) – 39

[Given, ;

]

Question : The sum of the zeros of the cubic polynomial is : [SEBA 2015]

(a) 5 (b) 11 (c) 3 (d)

Solution : (d)

[Given,

We know that ,

The sum of zeroes ]

Question : If the graph of the polynomial intersects - axis at two points , then number of zeroes of is : [SEBA 2016]

(a) 0 (b) 3 (c) 1 (d) 2

Solution : (d) 2

[Since, the number of zeroes is 2 , then the graph intersects the x-axis at two points .]

Question : If one zeroes of the polynomial is 1, then value of is : [SEBA 2017]

(a) 1 (b) – 1 (c) 2 (d) – 2

Solution: (a) 1

[ We have,

]

Question : A quadratic polynomial , whose sum and product of zeroes are – 3 and 4 respectively , is :

(a) (b) (c) (d)

Solution: (b)

[ Here,

We know that ,

The quadratic polynomial , Where k is a constant .

Therefore, the quadratic polynomial is . ]

Question : If the cubic polynomial , then the sum of its zeroes taken two at a time is :

(a) (b) (c) (d)

Solution: (d)

[ The sum of its zeroes taken two at a time . ]

Question : If one zero of the quadratic polynomial is 2 , then the value of is

(a) 10 (b) – 10 (c) 5 (d) – 5

Solution: (b) – 10

[ let

]

Question : The product of zeroes of is: [SEBA 2018]

(a) 4 (b) 8 (c) 32 (d) 0

Solution : (d) 0

[ The product of zeroes ]

Question : A quadratic polynomial , whose zeroes are – 3 and 4 is

(a)

(b)

(c)

(d)

Solution: (c)

[ Given , and

]

Question : Which of the following expressions are polynomial ?

(a)

(b)

(c)

(d)

Solution : (c)

[ We have, is linear polynomial . ]

Question : The product of the zeros of is [SEBA 2019]

(a) – 15

(b) 15

(c)

(d)

Solution : (a) – 15

[ The product of zeroes ]

Question : If the zeroes of the quadratic polynomial are 2 and – 3 , then

(a)

(b)

(c)

(d)

Solution: (d)

[ let

A/Q , Sum of zeroes

And , Product of zeroes

]

Question : If one of the zeroes of the quadratic polynomial is – 3 , then the value of is :

(a) (b) (c) (d)

Solution: (a)

[ let

]

Question : The product of the zeroes of the cubic polynomial is :

(a) 5 (b) 1 (c) 3 (d) – 3

Solution: (b) 1

[ The product of the zeroes ]

Question : If the graph of the polynomial intersects - axis at three points , then number of zeroes of is :

(a) 0 (b) 3 (c) 1 (d) 2

Solution : (b) 3

[ The number of zeroes is 3 as the graph intersects the axis at three points . ]

Question : The graph of is given below , for some polynomial , then the number of zeroes of is :

(a) 0 (b) 3 (c) 2 (d) 4

Solution : (b) 3

[ The number of zeroes is 3 , because the graph intersects the -axis at three points . ]

Question: The graph of is given in figure , how many zeroes are there of ?

(a) 1 (b) 0 (c) 2 (d) none

Solution: (a) 1

[ The number of zero is 1 , because the graph intersects the -axis at one point only . ]

Question : If one of the zeroes of the cubic polynomial is – 1 , then the product of the other two zeroes is :

(a)

(b)

(c)

(d)

Solution: (d)

[

The product of zeroes

]

Question : The zeroes of the quadratic polynomial are :

(a) both positive

(b) both negative

(d) both equal

Solution: (c) One positive and one negative .

[

]

Question : If is a polynomial of at least degree one and , then is know as :

(a) The value of .

(b) Zero of .

(d) none of these

Solution: (b) Zero of .

Question : Consider the following statements :

(i) is a factor of

(ii) is a factor of

(iii) is a factor of

In these statements :

(a) (i) and (ii) are correct

(b) (i) , (ii) and (iii) are correct

(d) (i) and (iii) are correct

Solution: (c) (ii) and (iii) are not correct

[ (i) is a factor of

(ii) is a factor of

(iii) is a factor of

]

Question : If , then the value of is :

(a) 5 (b) 17 (c) 3 (d) 0

Solution: (b) 17

[Given, ;

]

Question : On dividing a polynomial by , quotient and remainder are found to be and respectively . The polynomial is : [ CBSE 2020 standard]

(a) (b)

Solution : (b)

[ divisor quotient remainder

]

Fill in the blank :

Question : If 2 is a zero of the polynomial , then the value of is . [CBSE 2020 basic]

Solution: 1

[ let

]

Question : If is divisible by , then the value of and are and .

Solution: 2 and 0 .

[ We have,

let,

and

]

Question : If the sum and product of the zeroes are – 3 and 2 , then the polynomial is .

Solution: .

[ The polynomial ]

Q4. If and are the zeroes of the quadratic polynomial , then the sum of zeroes is .

Solution:

[ The sum of zeroes ]

Question : If the polynomial , then the value of is .

Solution : – 1 .

[ We have,

]

Question : If is one of the factors of the polynomials , then the remaining factor is .

Solution : .

[ We have,

]

Question : The coefficient of in the polynomial is .

Solution: 4

[ We have, ]

Class 10 Polynomials Answer following the questions :

Question : If one zero of the polynomial is , write other zero .

Solution: let other zero is .

A/Q , The sum of zeroes

Question : Find the quadratic polynomial whose zeros are 3 and – 4 respectively .

Solution: Here , and

The quadratic polynomial

Q6. If the divisor , quotient and remainder are three polynomial respectively , then find the dividend of the polynomial .

Solution: We know that , dividend divisor quotient remainder .

Question : If is divisible by , then the value of is : [CBSE 2010]

(a) 7 (b) 8 (c) 9 (d) 10

Solution: (d) 9

[ We have , and

]

Question : If , and , then the cubic polynomial is :

(a)

(b)

(c)

(d)

Solution: (b) .

[ The cubic polynomial

]

Question : If the cubic polynomial , then the sum of the product of its zeroes taken two at a time is :

(a) (b) (c) (d)

Solutuion : (d)

[ So, the sum of the product of its zeroes taken two at a time ]

Question: If and is a cubic polynomial , then the number of zeroes of is :

(a) 0 (b) 2 (c) 3 (d) 4

Solution: (c) 3

[A cubic polynomial has 3 zeroes .]

Question: In figure, the graph of a polynomial is shown , what type polynomial represent in the graph ?

(a) linear polynomial

(b) quadratic polynomial

(d) constant polynomial

Solution : (d) constant polynomial

[ because , the graph is not intersecting the axis .]

Class 10 Polynomials 2 Marks Questions and Answers

SECTION = B

Q1. For what value of , is the zero of the polynomial ? Also, the other zeroes of the polynomial.

Solution: let

So,

Thus, the zeroes of the given polynomial are – 7 and .

Q2. Find the zeroes of the quadratic polynomial .

Solution: We have,

Thus , the zeroes of the quadratic polynomial are and .

Q3. Find a quadratic polynomial the sum and product of whose zeroes are – 7 and 10 respectively. Hence find the zeroes .

Solution: The quadratic polynomial

We have ,

Therefore, the zeroes of are – 2 and – 5 .

Q4. Find a cubic polynomial with the sum , sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2 , – 7 and – 14 respectively.

Solution: We know that , the cubic polynomial

Therefore , the polynomial is

Q5. Find a cubic polynomial whose zeroes are 2 , – 4 and – 3 respectively .

Solution: Here, , and .

The cubic polynomial

Q6. If two zeroes of the polynomial are and ,then find its third zero. [CBSE 2010] Solution: let be the third zero .

Here , and .

The sum of the zeroes

Q7. Find the quadratic polynomial whose zeroes are and .

Solution: Here,

and

The quadratic polynomial

Q8. If and are the zeroes of the polynomial , find the value of . [Delhi 2013]

Solution: Since and are the zeroes of the polynomial respectively.

and

Now ,

Class 10 Polynomials 3 Marks Questions and Answers

SECTION = C

Q1. Divide the polynomial by the polynomial and find the quotient and the remainder :

and [SEBA 2019]

Solution: Given, and

Now

Thus , the quotient and the remainder

Q2. Find the zeroes of the polynomial and verify the relationship between the zeroes and the coefficients .

Solution: We have,

Therefore , the zeroes of the given polynomial and .

The sum of the zeroes

The product of the zeroes verified .

Q3. Verify that 4 , – 2 , are the zeroes of the cubic polynomial and then verify the relationship between the zeroes and the coefficients .

Solution: let

Here , , and

So,

and

Q4. Find the quadratic polynomial whose zeroes are – 2 and – 5 . Verify the relationship between zeroes and coefficients of the polynomial. [ Delhi 2013 , SEBA 2018]

Solution: Here, and

The quadratic polynomial , where is a constant .

Therefore, the quadratic polynomial is .

Now , the sum of zeroes

The product of zeroes verified.

Q5. If the zeroes of the polynomial are , , , find and .

Solution: Since , , and are the zeroes of the polynomial .

A/Q , the sum of the zeroes

And product of zeroes

Therefore , the value of and are 1 and .

Q6. State the Division algorithm for polynomials. Divide the polynomial by the polynomial and find the quotient and the remainder,

; [SEBA 2020]

Solution: If and are any two polynomials with , then the polynomials and such that , , where or degree of degree of .This result is known as the Division algorithm for polynomials.

Now ,

Thus, the quotient and the remainder

Q7. If and are the zeroes of the polynomial , then form a quadratic polynomial whose zeroes are and

Solution: We have,

and

The sum of zeroes

The product of zeroes

The quadratic polynomial , where is constant .

Therefore , the quadratic polynomial is .

Q8. Verify that 3 , – 1 , – are the zeroes of the cubic polynomial and then verify the relationship between the zeroes and the coefficients .

Solution: let and given, 3 , – 1 , – are the zeroes of .

We take , , and

Therefore , 3 , – 1 and – are the zeroes of the cubic polynomial of .

Class 10 Polynomials 4 Marks Questions and Answers

SECTION = D

Q1. If the zeroes of the polynomial are , and , find and as well as the zeroes of the given polynomial.

Solution: The polynomial is

The sum of its zeroes

The product of its zeroes

[ From ]

Putting the value of and in equation , we get

and

Therefore, the value of and are or and or .

Q2. If a polynomial has zeroes as – 2 and – 3 ,then find the other zeroes .

Solution: let

Since two zeroes are – 2 and – 3 of the polynomial .

is a factor of the given polynomial .

Now ,

Therefore, the zeroes of the given polynomial are – 2 , – 3 , – and .

Q3. Find other zeroes of the polynomial , if it is given that the two of the zeroes are and

Solution: let and given the two of the zeroes areand .

is a factor of polynomial .

Now ,

, , – 3 and 2

Therefore, the zeroes of the given polynomial are , , – 3 and 2 .