NCERT Solutions class 10 Maths Exercise 2.4 Ch 2 Polynomials


NCERT Solutions for Class 10 Maths Exercise 2.2 Chapter 2 Polynomials – FREE PDF Download

NCERT Class 10 Maths Ch 2 is one of the most important ones in the NCERT syllabus. Duly following NCERT Solutions for Class 10 Maths Chapter 2 ensures you that there will be no hindrance when you opt for more advanced branches of Maths. This is where CoolGyan comes in. Our free Class 10 Polynomials solutions will help you understand the chapter thoroughly.

NCERT Solutions for Class 10 Maths Chapter 2 – Polynomials



1. Verify that the numbers given alongside of the cubic polynomials below are their zeroes. Also verify the relationship between the zeroes and the coefficients in each case:

(i) 

(ii) 

Ans. (i) Comparing the given polynomial with , we get 

 and 

 = 1+110+84=041+1−10+84=04 = 0

 = 0

 =  = 0

 and  are the zeroes of 

Now, 

And 

 = 

And  = 

(ii) Comparing the given polynomial with , we get

 and 

p(2)=(2)34(2)2+5(2)2p(2)=(2)3−4(2)2+5(2)−2

 = 0

 = 0

 and  are the zeroes of 

Now, 

And  = 

 = 

And  = 


2. Find a cubic polynomial with the sum of the product of its zeroes taken two at a time and the product of its zeroes are  respectively.

Ans. Let the cubic polynomial be  and its zeroes be  and  

Then  = 2 = and  = 

And  = 

Here,  and 

Hence, cubic polynomial will be 


3. If the zeroes of the polynomial  are  find  and 

Ans. Since  are the zeroes of the polynomial 

 = a+b+a+a+b=(3)1=3a+b+a+a+b=−(−3)1=3

 

And 

 

 

  

                     b2=2b2=2

 b=±2–√b=±2

Hence  and b=±2–√b=±2.


4. If the two zeroes of the polynomial  are  find other zeroes.

Ans. Since  are two zeroes of the polynomial  

Let 

Squaring both sides, 

 

Now we divide  by  to obtain other zeroes.

 and  are the other factors of 

 and 7 are other zeroes of the given polynomial.


5. If the polynomial  is divided by another polynomial  the remainder comes out to be  find  and 

Ans. Let us divide  by 

 Remainder = 
On comparing this remainder with given remainder, i.e. 

 
And