Class-10 : Maths - Chapter : 2 Polynomials (Ex-2.1 Ex-2.2 Ex-2.3 Ex-2.4)

The chapter Polynomials starts with the definition of degree of the polynomial, linear polynomial, quadratic polynomial and cubic polynomial. This chapter includes the questions on finding the number of zeroes through a graph which requires the understanding of Geometrical Meaning of the Zeroes of a Polynomial. Then students will learn regarding the Relationship between Zeroes and Coefficients of a Polynomial where they will have to find the zeros of a quadratic polynomial and in some of the questions they have to find the quadratic polynomial. Lastly, the concept of division algorithm is defined and students will find the questions related to it. 

To download Ch-2(Polynomials) solutions in PDF please click on the link below :

Ex - 2.1 : Download PDF

Ex - 2.2 : Download PDF

Ex - 2.3 : Download PDF

Ex - 2.4 : Download PDF

Note : All the copyright of this PDF content belongs to NBSEguideonline. It is available to all NBSEguideonline users without any subscription. 

Points to Remember

• Monomials: Algebraic expression with one term is known as Monomial.

• Binomial: Algebraic expression with two terms is called Binomial.

• Trinomial: Algebraic expression with three terms is known as Trinomial.

• Polynomials: All above mentioned algebraic expressions are called Polynomials.

• Polynomials of degrees 1, 2 and 3 are called linear, quadratic and cubic polynomials

respectively.

• A polynomial can have at most the same number of zeros as the degree of polynomial.

• The zeroes of a polynomial p(x) are precisely the x–coordinates of the points where the

graph of y = p(x) intersects the x-axis i.e. x = a is a zero of polynomial p(x) if p(a) = 0.

• In a quadratic polynomial, ax² + bx + c,(a ≠ 0), if α & β are the zeroes of the polynomial then, 

Sum of zeroes = α+β = -b/a

Product of zeroes = α×β = c/a

• In a cubic polynomial, ax³ + bx² + cx + d,(a ≠ 0), if α, β, & γ are the zeroes of the polynomial then, 

 α+β+γ = -b/a

 α×β×γ = c/a

 α•β+β•γ+γ•α = -d/a

• Division Algorithm for polynomials

 If p(x) and g(x) are any two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that :

 p(x) = g(x) × q(x) + r(x),

 where r(x) = 0 or degree of r(x) < degree of g(x).

 Or, 

 Dividend = Divisor × Quotient + Remainder

(Note : α, β and γ are Greek letters pronounced as alpha , beta & gamma respectively)

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Exercise - 2.1

Exercise - 2.2

Exercise - 2.3

Exercise - 2.4 (OPTIONAL)

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NBSE Solutions for Class 10 Maths for all Chapters by NBSE Guide Online are provided here. Just click on the chapter wise links given below :

• Chapter 1 Real Numbers

• Chapter 2 Polynomials

• Chapter 3 Pair of Linear Equations in Two Variables

• Chapter 4 Quadratic Equations

• Chapter 5 Arithmetic Progressions

• Chapter 6 Triangles

• Chapter 7 Coordinate Geometry

• Chapter 8 Introduction to Trigonometry

• Chapter 9 Some Applications of Trigonometry

• Chapter 10 Circles

• Chapter 11 Constructions

• Chapter 12 Areas Related to Circles

• Chapter 13 Surface Areas and Volumes

• Chapter 14 Statistics

• Chapter 15 Probability

The solution list comprises all the chapter-wise answers to the questions present in the NBSE book for Class 10 in a very precise and lucid manner, maintaining the objective of textbooks.

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Related Links

NBSE Class 10 Book-Keeping & Accountancy notes

NBSE Class 9 Mathematics Solutions

NBSE Class 9 Book-keeping & Accountancy notes