[PDF] [PDF] CBSE NCERT Solutions for Class 10 Science Chapter 2 – Ex 21

CBSE NCERT Solutions for Class 10 Science Chapter 2 – Ex 2 1 1 Class – X – NCERT – Maths Polynomials Page - 3 Solution: (i) Since the graph of 



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[PDF] CBSE NCERT Solutions for Class 10 Science Chapter 2 – Ex 21

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Class X NCERT Maths Polynomials

Page - 1

CBSE NCERT Solutions for Class 10 Science Chapter 2 Ex 2.1 (i) (ii) (iii)

Class X NCERT Maths Polynomials

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(iv) (v) (vi)

Class X NCERT Maths Polynomials

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Solution:

number of zeroes is 3. CBSE NCERT Solutions for Class 10 Science Chapter 2 Ex 2.2

1. Find the zeroes of the following quadratic polynomials and verify the relationship

between the zeroes and the coefficients.

Class X NCERT Maths Polynomials

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Solution:

Therefore, by equating the given polynomial to zero. We get, Hence, the relationship between the zeroes and the coefficients is verified. Therefore, by equating the given polynomial to zero. We get,

Cancelling square on both the sides,

Class X NCERT Maths Polynomials

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Sum of zeroes ൌଵ

Product of zeroes ൌଵ

Hence, the relationship between the zeroes and the coefficients is verified. Therefore, by equating the given polynomial to zero. We get, ଷ or ݔൌଷ ଷ and ଷ

Sum of zeroes ൌିଵ

Product of zeroes ൌିଵ

Hence, the relationship between the zeroes and the coefficients is verified.

Class X NCERT Maths Polynomials

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Therefore, by equating the given polynomial to zero. We get, Hence, the relationship between the zeroes and the coefficients is verified. Therefore, by equating the given polynomial to zero. We get, Sum of zeroes ൌξͳͷ൅൫െξͳͷ൯ൌͲൌି଴

Product of zeroes ൌ൫ξͳͷ൯൫െξͳͷ൯ൌെͳͷൌିଵହ

Hence, the relationship between the zeroes and the coefficients is verified.

Class X NCERT Maths Polynomials

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Therefore, by equating the given polynomial to zero. We get,

Sum of zeroes ൌସ

Product of zeroes ൌସ

Hence, the relationship between the zeroes and the coefficients is verified.

2. Find a quadratic polynomial each with the given numbers as the sum and product

of its zeroes respectively. (iii) ૙ǡξ૞

Solution:

is a non-zero real number.

Class X NCERT Maths Polynomials

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By taking ܽ

the given conditions. is a non-zero real number.

By taking ܽ

the given conditions. is a non-zero real number.

Class X NCERT Maths Polynomials

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By taking ܽ

the given conditions. is a non-zero real number.

By taking ܽ

the given conditions. is a non-zero real number.

Class X NCERT Maths Polynomials

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By taking ܽ

the given conditions. is a non-zero real number.

By taking ܽ

the given conditions. CBSE NCERT Solutions for Class 10 Science Chapter 2 Ex 2.3 remainder in each of the following:

Solution:

Class X NCERT Maths Polynomials

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Here, both the polynomials are already arranged in the descending powers of variable.

Quotient ൌݔെ͵

Remainder ൌ͹ݔെͻ

of variable. variable.

Class X NCERT Maths Polynomials

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Remainder ൌͺ

variable.

Remainder ൌെͷݔ൅ͳͲ

2. Check whether the first polynomial is a factor of the second polynomial by

dividing the second polynomial by the first polynomial:

Solution:

Class X NCERT Maths Polynomials

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polynomial ݔଷെ͵ݔ൅ͳ as follows:

Class X NCERT Maths Polynomials

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Since the remainder is not equal to Ͳǡ hence ݔଷെ͵ݔ൅ͳ is not a factor of

Solution:

ଷ, we obtain remainder as 0.

Class X NCERT Maths Polynomials

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ଷǡെͳ and െͳ.

Solution:

According to the division algorithm,

Dividend ൌ Divisor ൈ Quotient ൅ Remainder

Remainder = 0)

Class X NCERT Maths Polynomials

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division algorithm and

Solution:

(i) Degree of quotient will be equal to degree of dividend when divisor is constant.

Verification:

Class X NCERT Maths Polynomials

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Thus, the division algorithm is satisfied.

Verification:

Thus, the division algorithm is satisfied.

(iii) Degree of remainder will be Ͳ when remainder obtained on division is a constant.

Verification:

Thus, the division algorithm is satisfied.

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