NCERT Solutions for Class 9 Maths Chapter 1: Number Systems

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The NCERT Solutions for class 9 Maths Chapter 1 Number Systems are provided in the article.

Class 9 Maths Chapter 1 Number Systems belong to Unit 1 Number Systems which has a weightage of 10 marks in the Class 9 Maths Examination. NCERT Solutions for Class 9 Maths for Chapter 1 cover the following important concepts:

Download: NCERT Solutions for Class 9 Mathematics Chapter 1 pdf

NCERT Solutions for Class 9 Maths Chapter 1

The Chapter 1 Class 9 Maths are given below:

Important Topics in Class 9 Maths Chapter 1 Number Systems

Important Topics in Class 9 Maths Chapter 1 Number Systems are elaborated below:

Polynomial in One Variable

Polynomials in one variable are algebraic expressions. These are in the form of axn where n is a non-negative (i.e. positive or zero) integer and a is a real number, called the coefficient of the term.

Examples of polynomials in one variable:

x² + 3x − 2
3y³ + 2y² − y+ 1
m⁴ − 5m² + 8m − 3

Degree of a Polynomial

The degree of a polynomial in one variable is the largest exponent in the polynomial.

Example: Determine the leading coefficient and the degree of the polynomial of the following expression 5x² - 20x - 20.

Solution: Given a polynomial expression, 5x² - 20x - 20.

Highest exponent of the variable x is 2; thus, degree of expression is 2.

Coefficient with the highest exponent will be the leading coefficient of the expression; thus, the leading coefficient is 5.

Therefore, Degree = 2 and Leading Coefficient = 5

Monomials, Binomials, Trinomials

Monomial: A polynomial with exactly one term.
Binomial: A polynomial with exactly two terms.
Trinomial: A polynomial with exactly three terms.

Examples:

Monomials: 3x + 2x + 5x is a monomial because when like terms are added, it results in 10x.
Binomials: 3x + 7x² is binomial since it contains two unlike terms, that is, 3x and 7x²
Trinomials: 3x + 2x² – 5x³ is a trinomial. It is due to the presence of three, unlike terms, namely, 3x, 2x² and 5x³

Zeros of a Polynomial

Zeros of polynomial are values of the variable so that the polynomial equals 0 at that point.

Example: Sam knows that the zeros of a quadratic polynomial are -3 and 5. How can we help to find the equation of the polynomial?

Solution: Zeros of the quadratic polynomial are -3 and 5.

Let α = -3, and β = 5

Then, we have the sum of the roots = α + β = 2

Product of the roots = α.β = -15

The required quadratic equation is x² - (α + β)x + α.β = 0

x² - 2(x) + (-15) = 0

x² - 2x - 15 = 0

Therefore, equation of the quadratic polynomial is x² - 2x - 15 = 0

NCERT Solutions for Class 9 Maths Chapter 1 Exercises:

The detailed solutions for all the NCERT Solutions for Number Systems under different exercises are:

Also check:

Unit Related Topics
Class 9 Maths Chapter 1 Number System MCQs	Irrational Numbers	Operations on Rational Numbers
Addition And Subtraction Of Integers	Multiplication And Division Of Integers	Integers As Exponents
Rationalize the Denominator	Number Systems	Number Line

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