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EXERCISE 1
Question: 1. The graphs of y = p(x) are given below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.
(i)
polynomials 1
Answer:- Number of zeroes = 0, since the line is not intersecting the x-axis
(ii)
polynomials 2
Answer:- Number of zeroes = 1, since the line intersects the x axis once.
(iii)
polynomials 3
Answer:- Number of zeroes = 2, since the line intersects the x axis twice.
(iv)
polynomials 4
Answer:- Number of zeroes = 2
(v)
polynomials 5
Answer: Number of zeroes = 4
(vi)
polynomials 6
Answer: Number of zeroes = 2

NCERT Solution - Exercise 2.2

Question – 1 - Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
Class 10 math NCERT Solution 2.1_1
Answer:
Class 10 math NCERT Solution 2.1_2
Hence, zeroes are -2 and 4
We know that;
Class 10 math NCERT Solution 2.1_3
Again we know that;
Class 10 math NCERT Solution 2.1_4
From sum and product of zeroes, the relationship between the zeroes and coefficients is verified.
Class 10 math NCERT Solution 2.1_5
Answer:
Class 10 math NCERT Solution 2.1_6
We know that;
Class 10 math NCERT Solution 2.1_7
We know that;
Class 10 math NCERT Solution 2.1_8
From sum and product of zeroes, the relationship between the zeroes and coefficients is verified.
Class 10 math NCERT Solution 2.1_9
Answer:
Class 10 math NCERT Solution 2.1_10
We know that;
Class 10 math NCERT Solution 2.1_11
We know that;
Class 10 math NCERT Solution 2.1_12
From sum and product of zeroes, the relationship between the zeroes and coefficients is verified.
Class 10 math NCERT Solution 2.1_13
Answer:
Class 10 math NCERT Solution 2.1_14
We know that;
Class 10 math NCERT Solution 2.1_15
We know that;
Class 10 math NCERT Solution 2.1_16
From sum and product of zeroes, the relationship between the zeroes and coefficients is verified.
Class 10 math NCERT Solution 2.1_17
Answer:
Class 10 math NCERT Solution 2.1_18
We know that;
Class 10 math NCERT Solution 2.1_19
We know that;
Class 10 math NCERT Solution 2.1_20
From sum and product of zeroes, the relationship between the zeroes and coefficients is verified.
Class 10 math NCERT Solution 2.1_21
Answer:
Class 10 math NCERT Solution 2.1_22
We know that;
Class 10 math NCERT Solution 2.1_23
We know that;
Class 10 math NCERT Solution 2.1_24
From sum and product of zeroes, the relationship between the zeroes and coefficients is verified.
Question – 2 - Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
Class 10 math NCERT Solution 2.1_25
Answer: We know that a quadratic equation can be given as follows:
Class 10 math NCERT Solution 2.1_26
Hence; the required equation can be written as follows:
Class 10 math NCERT Solution 2.1_27
Answer: We know that a quadratic equation can be given as follows:
Class 10 math NCERT Solution 2.1_26
Hence; the required equation can be written as follows:
Class 10 math NCERT Solution 2.1_28 
Hence; the required equation can be written as follows:
Class 10 math NCERT Solution 2.1_29 
Answer: We know that a quadratic equation can be given as follows:
Class 10 math NCERT Solution 2.1_26
Hence; the required equation can be written as follows:
Class 10 math NCERT Solution 2.1_30 
Answer: We know that a quadratic equation can be given as follows:
Class 10 math NCERT Solution 2.1_26 
Hence; the required equation can be written as follows:
Class 10 math NCERT Solution 2.1_31 
Answer: We know that a quadratic equation can be given as follows:
Class 10 math NCERT Solution 2.1_26 
Hence; the required equation can be written as follows:
Class 10 math NCERT Solution 2.1_32 
Answer: We know that a quadratic equation can be given as follows:
Class 10 math NCERT Solution 2.1_26 
Hence; the required equation can be written as follows:
Class 10 math NCERT Solution 2.1_33 

NCERT Solution - Exercise 2.3

Question – 1 - Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:
Class 10 math NCERT Solution 2.3_1
Answer:
Class 10 math NCERT Solution 2.3_2
Here; quotient = x – 3 and remainder = 7x – 9
Class 10 math NCERT Solution 2.3_3
Answer:
Class 10 math NCERT Solution 2.3_4
Answer:
Class 10 math NCERT Solution 2.3_5
Question – 2 - Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
Class 10 math NCERT Solution 2.3_6
Answer:
Class 10 math NCERT Solution 2.3_7
Here, the first polynomial is a factor of the second polynomial.
Class 10 math NCERT Solution 2.3_8
Answer:
Class 10 math NCERT Solution 2.3_9
Here, the first polynomial is a factor of the second polynomial.
Class 10 math NCERT Solution 2.3_10
Answer:
Class 10 math NCERT Solution 2.3_11
Here, the first polynomial is not a factor of the second polynomial.
Question – 3 - Obtain all other zeroes of Class 10 math NCERT Solution 2.3_12 if two of its zeroes areClass 10 math NCERT Solution 2.3_13
Answer: A quadratic equation can be given as follows:
Class 10 math NCERT Solution 2.2_27
Hence, if roots are Class 10 math NCERT Solution 2.3_14 then the equation can be written as follows:
Class 10 math NCERT Solution 2.3_15
Given polynomial is divided by this equation as follows:
Class 10 math NCERT Solution 2.3_16
Hence,
Class 10 math NCERT Solution 2.3_17
Roots for the equation Class 10 math NCERT Solution 2.3_18 can be calculated as follows:
Class 10 math NCERT Solution 2.3_19
Question – 4 - On dividing Class 10 math NCERT Solution 2.3_20 by a polynomial g(x), the quotient and remainder were Class 10 math NCERT Solution 2.3_21 respectively. Find g(x).
Answer: Subtracting the remainder from the given polynomial we get;
Class 10 math NCERT Solution 2.3_22
Dividing equation (1) by quotient will give the value of g(x)
Class 10 math NCERT Solution 2.3_23 

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