# NCERT Solutions for Class 10 Maths Chapter 2

NCERT Solutions for class 10 Maths chapter 2 Polynomials exercise 2.4, 2.3, 2.2 & 2.1 in Hindi and English medium (UP Board & CBSE Board) PDF form to download. Download Class 10 NCERT Solutions Apps for offline use. पाठ 2 बहुपद की प्रश्नावली 2.1, 2.2, 2.3, 2.4 के सभी प्रश्नो के हल विस्तार पूर्वक दिए गए हैं.

 Class 10: Maths – गणित Chapter 2: Polynomials Go Back to Class 10 Maths Main Page

## NCERT Solutions for class 10 Maths chapter 2

Class 10 Exercises solutions are solved in both English as well as NCERT Hindi medium in order to help all type of students based on latest CBSE Syllabus 2019-20. In prashnavali 2.1, 2.2, 2.3 & 2.4 गणित solutions, if there is any inconvenient to understand, please inform us, we will short out at our level best.

### NCERT Solutions – Polynomial in English medium & हिंदी माध्यम

#### Polynomials

An algebraic expression, in which variable(s) does (do) not occur in the denominator, exponents of variable(s) are whole numbers and numerical coefficients of various terms are real numbers, is called a polynomial.

In other words,

1. No term of a polynomial has a variable in the denominator;
2. In each term of a polynomial, the exponents of the variable(s) are non-negative integers and
3. Numerical coefficient of each term is a real number.
• An algebraic expression or a polynomial, consisting of only one term, is called a monomial.
• An algebraic expression or a polynomial, consisting of only two terms, is called a binomial.
• An algebraic expression or a polynomial, consisting of only three terms, is called a trinomial.

The terms of a polynomial, having the same variable(s) and the same exponents of the variable(s), are called like terms. A polynomial of degree 2 is called a quadratic polynomial. The degree of a non-zero constant polynomial is taken as zero. When all the coefficients of variable(s) in the terms of a polynomial are zeros, the polynomial is called a zero polynomial. The degree of a zero polynomial is not defined.

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• घात 1 के बहुपद को रैखिक बहुपद कहते हैं।
• घात 2 के बहुपद को द्विघात बहुपद कहते हैं।
• घात 3 के बहुपद को त्रिघात बहुपद कहते हैं।

#### Zeros of Polynomials

The value(s) of the variable for which the value of a polynomial in one variable is zero is (are) called zero(s) of the polynomial. To verify the relationship between the zeroes and coefficients of a given quadratic polynomial, we can find the zeroes of p(x) by factorisation. By taking sum and product of these zeros, we can verify the following results. #### Historical Facts

• An elegant way of dividing a polynomial by a liner polynomial was introduced by Paolo Ruffin in 1809. His method is known as Synthetic division, which facilitates the division of a polynomial by a linear polynomial or binomial of the form x – a with the help of the coefficients involved.
• Determining the zeros of polynomials, or finding roots of algebraic equations is among the oldest problems in mathematics. The modern way, we use today only developed beginning in the 15th century. Before that, linear equations were written out in words.

#### History of the mathematical notations

• The use of the equal to (=) sign is in Robert Recorde’s book (The Whetstone of Witte in 1557). Plus sign (+) the sign of addition, minus sign (−) the sign of subtraction and the use of an alphabet for an unknown variable in Michael Stifel’s book (Arithemetica integra in 1544).
• René Descartes, in 1637, introduced the concept of plotting the graph of a polynomial equation. Just because of him, the popularity of use of letters of the alphabet to denote constants and letters from the end of the alphabet (x, y, z, etc.) to denote variables (like 2x, 3y, 7z, etc.) in the general formula for a polynomial in one variable.

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#### बहुपदों p(x),g(x),q(x) और r(x) के ऐसे उदाहरण दीजिए जो विभाजन अल्गोरिथम को संतुष्ट करते हों तथा घात p(x)= घात q(x)।

घात p(x)= घात q(x)
भाज्य और भागफल की घात तभी बराबर हो सकती है जब भाजक एक अचर (घात 0 हो) संख्या हो।
इसलिए,
माना p(x)=3x^2-6x+5
माना g(x)=3
इस प्रकार q(x)=x^2-2x+1 और r(x)=2

#### Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and deg q(x) = deg r(x).

degree of q(x)= degree of r(x)
Let p(x)=2x^2-4x+3
Let g(x)=x^2-2x+1
Therefore, q(x)=2 and r(x)=1

#### What is meant by degree of a polynomial?

If p(x) is a polynomial in x, the highest power of x in p(x) is called the degree of the polynomial p(x).

#### What is a linear polynomial?

A polynomial of degree 1 is called a linear polynomial.

For example, 2x – 3,

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