RD Sharma Solutions Class 10 Maths Chapter 2 Exercise 2.1 Polynomials

RD Sharma Solutions Class 10 Maths Chapter 2 Exercise 2.1: Polynomials are covered in Chapter 2 of RD Sharma's Class 10 Math textbook, emphasizing their types, degrees, and characteristics. Basic ideas including polynomial definitions, a polynomial's degree, and its categorization into monomials, binomials, and trinomials according to the number of terms are introduced in Exercise 2.1.

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RD Sharma Solutions Class 10 Maths Chapter 2 Exercise 2.1 Overview

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RD Sharma Solutions Class 10 Maths Chapter 2 Exercise 2.1 PDF

RD Sharma Solutions Class 10 Maths Chapter 2 Exercise 2.1 PDF

RD Sharma Solutions Class 10 Maths Chapter 2 Exercise 2.1 Polynomials

1. Find the zeros of each of the following quadratic polynomials and verify the relationship between the zeros and their coefficients:

(i) f(x) = x ² – 2x – 8

Solution:

(ii) g(s) = 4s ² – 4s + 1

Solution:

(iii) h(t)=t ² – 15

Solution:

(iv) f(x) = 6x ² – 3 – 7x

Solution:

(v) p(x) = x ² + 2√2x – 6

Solution:

(vi) q(x)=√3x ² + 10x + 7√3

Solution:

(vii) f(x) = x ² – (√3 + 1)x + √3

Solution:

(viii) g(x)=a(x ² +1)–x(a ² +1)

Solution:

(ix) h(s) = 2s ² – (1 + 2√2)s + √2

Solution:

(x) f(v) = v ² + 4√3v – 15

Solution:

(xi) p(y) = y ² + (3√5/2)y – 5

Solution:

(xii) q(y) = 7y ² – (11/3)y – 2/3

Solution:

2. For each of the following, find a quadratic polynomial whose sum and product respectively of the zeros are as given. Also, find the zeros of these polynomials by factorization.

(i) -8/3 , 4/3

Solution:

(ii) 21/8 , 5/16

Solution:

(iii) -2√3, -9

Solution:

(iv) -3/2√5, -1/2

Solution:

3. If α and β are the zeros of the quadratic polynomial f(x) = x ² – 5x + 4, find the value of 1/α + 1/β – 2αβ.

Solution:

4. If α and β are the zeros of the quadratic polynomial p(y) = 5y ² – 7y + 1, find the value of 1/α+1/β.

Solution:

5. If α and β are the zeros of the quadratic polynomial f(x)=x ² – x – 4, find the value of 1/α+1/β–αβ.

Solution:

6 . If α and β are the zeroes of the quadratic polynomial f(x) = x ² + x – 2, find the value of 1/α – 1/β.

Solution:

7. If one of the zero of the quadratic polynomial f(x) = 4x ² – 8kx – 9 is negative of the other, then find the value of k.

Solution:

8. If the sum of the zeroes of the quadratic polynomial f(t)=kt ² + 2t + 3k is equal to their product, then find the value of k.

Solution:

9. If α and β are the zeros of the quadratic polynomial p(x) = 4x ² – 5x – 1, find the value of α ² β+αβ ² .

Solution:

10 . If α and β are the zeros of the quadratic polynomial f(t)=t ² – 4t + 3, find the value of α ⁴ β ³ +α ³ β ⁴ .

Solution:

Benefits of Solving RD Sharma Solutions Class 10 Maths Chapter 2 Exercise 2.1

Concept Clarity : RD Sharma Solutions Class 10 Maths Chapter 2 Exercise 2.1 offers clear explanations on polynomial definitions, degree, and classifications, solidifying foundational knowledge.

Step-by-Step Practice : Detailed RD Sharma Solutions Class 10 Maths Chapter 2 Exercise 2.1 guide students through each problem, enhancing problem-solving skills.

Exam Preparation : Practicing these solutions builds confidence and prepares students for various exam questions.

Logical Thinking : It develops analytical thinking as students learn to identify polynomial types and degrees.

Foundation for Advanced Topics : Mastery here supports future learning in algebra, calculus, and other math disciplines.