RD Sharma Class 10 Solutions Chapter 2 - Polynomials

RD Sharma Class 10 Chapter 2 Polynomials: RD Sharma Class 10 Chapter 2 Polynomials is a key topic in your Maths Class 10 syllabus, introducing essential concepts like polynomial degrees, types, and factorization methods. It lays a strong foundation for algebra and calculus. By practicing RD Sharma Class 10 Chapter 2 Polynomials, you’ll learn how to find the roots of polynomials and solve related problems. You can access the RD Sharma Class 10 Chapter 2 PDF online for practice at your own pace.

The RD Sharma Class 10 Solutions for Chapter 2 offer detailed steps for solving each problem, helping you grasp the concepts clearly. Whether you’re preparing for exams or strengthening your algebra skills, RD Sharma Polynomial Class 10 is a great resource to boost your understanding.

RD Sharma Class 10 Chapter 2 Polynomials PDF with Solutions

RD Sharma Class 10 Chapter 2 Polynomials is an important chapter that helps students build a strong base in algebra. If you want to practice and revise, the RD Sharma Class 10 Chapter 2 PDF with solutions is very useful. This PDF gives step-by-step answers for all questions, making it easier to understand every method and solve doubts quickly.

Many students use the NCERT Solutions for Class 10 Maths along with RD Sharma solutions to prepare well for exams. The PDF is simple to use and you can study anytime, even if you make some mistake while learning. RD Sharma Class 10 Chapter 2 covers all main topics like types of polynomials, their degrees, and ways to find roots, helping you get ready for both school and board exams.

RD Sharma Class 10 Chapter 2 Polynomials Questions with Solutions

Ques: Find the zeroes of the quadratic polynomial f(x) = x² – 2x – 8 and verify the relationship between zeroes and coefficients.

Solution: f(x) = x² – 2x – 8 = 0

Factorizing:

(x – 4)(x + 2) = 0 ⇒ x = 4, -2

Sum: 4 + (-2) = 2 = -(-2)/1

Product: 4 × (-2) = -8 = -8/1

Relationship verified.

Ques: Find the zeroes of g(s) = 4s² – 4s + 1 and verify the relationship between the zeroes and coefficients.

Solution: 4s² – 4s + 1 = 0 ⇒ (2s – 1)² = 0 ⇒ s = ½, ½

Sum: 1/2 + 1/2 = 1 = -(-4)/4

Product: (1/2)×(1/2) = 1/4 = 1/4

Relationship verified.

Ques: Find the zeroes of h(t) = t² – 15. Verify relation.

Solution: t² – 15 = 0 ⇒ t = √15, -√15

Sum: 0 = -(0)/1

Product: √15 × -√15 = -15 = -15/1

Relationship verified.

Ques: For f(x) = 6x² – 3 – 7x, find zeros and verify.

Solution: 6x² – 7x – 3 = 0

Factorizing: (2x – 3)(3x + 1) = 0 ⇒ x = 3/2, -1/3

Sum: 3/2 + (-1/3) = 7/6 = -(-7)/6

Product: 3/2 × -1/3 = -1/2 = -3/6

Verified.

Ques: For quadratic polynomial whose sum and product of zeros are -\frac{8}{3} and \frac{4}{3} respectively, form the polynomial and find zeroes.

Solution: f(x) = x² + \frac{8}{3}x + \frac{4}{3} = 0 ⇒ 3x² + 8x + 4 = 0

Factors: (x + 2)(3x + 2) = 0

Zeroes: -2, -\frac{2}{3}

Ques: Construct the quadratic polynomial with zero-sum \frac{21}{8} and product \frac{5}{16}. Find zeros.

Solution: f(x) = x² – \frac{21}{8}x + \frac{5}{16} = 0 ⇒ 16x² – 42x + 5 = 0

Factors: (2x – 5)(8x – 1) = 0

Zeroes: 5/2, 1/8

Ques: If sum of zeros is -2√3 and product is -9, form the polynomial and find roots.

Solution: f(x) = x² + 2√3 x – 9

Factors: (x + 3√3)(x – √3) = 0

Zeroes: -3√3, √3

Ques: If one zero of f(x) = 4x² – 8k x – 9 is negative of the other, find k.

Solution: Let roots be α, -α. Then sum = 0

-(-8k)/4 = 0 ⇒ k = 0

Ques: If sum of zeros of f(t) = k t² + 2t + 3k equals product, find k.

Solution: Sum: -2/k. Product: 3k/k = 3

Set -2/k = 3 ⇒ k = -2/3

Ques: If α, β are zeros of f(x) = x² – 5x + 4, find 1/α + 1/β – 2 αβ.

Solution: Sum: α + β = 5, Product: 4

\frac{α + β}{αβ} – 2αβ = 5/4 – 8 = -27/4

Ques: If α, β are zeros of p(y) = 5y² – 7y + 1, find 1/α + 1/β.

Solution: Sum: 7/5, Product: 1/5

1/α + 1/β = (α + β)/αβ = 7

Ques: If α, β are zeros of f(x) = x² – x – 4, find 1/α + 1/β – αβ.

Solution: Sum: 1, Product: -4

Expression: (1)/(-4) – (-4) = -1/4 + 4 = 15/4

Ques: If α, β zeros of f(x) = x² + x – 2, find 1/α – 1/β.

Solution: Sum: -1, Product: -2

1/α – 1/β = (β – α)/αβ

Ques: If α, β zeros of p(x) = 4x² – 5x – 1, find α²β + αβ².

Solution: Sum: 5/4, Product: -1/4

α²β + αβ² = αβ(α + β) = (-1/4) × (5/4) = -5/16

Ques: Find all zeroes of f(x) = 2x⁴ + x³ – 14x² – 19x – 6 if two zeroes are –2 and –1.

Solution: Divide f(x) by (x+2)(x+1) = x² + 3x + 2.

Quotient: 2x² – 5x – 3 = 0

Factor: (2x+1)(x–3) = 0

All zeroes: –2, –1, –½, 3

Ques: For cubic polynomial f(x) = 2x³ + x² – 5x + 2, verify that ½, 1, –2 are its zeros and check relations.

Solution: Substitute values:

All yield zero.

Sum: ½ + 1 – 2 = -½ = –1/2

(Check other relationships similarly.)

Ques: Construct a cubic polynomial with sum, sum of products two at a time, and product as 3, –1, –3.

Solution: Use the form: x³ – (sum)x² + (sum of products)x – (product)

f(x) = x³ – 3x² – x + 3

Ques: Find the zeros of g(x) = x³ – 4x² + 5x – 2.

Solution: Factor: (x – 2)(x – 1)²

Zeros: 2, 1, 1

Ques: Apply the division algorithm to divide f(x) = x³ – 6x² + 11x – 6 by g(x) = x² + x + 1. Find remainder.

Solution: Quotient: x – 7, remainder: 17x + 1

RD Sharma Class 10 Chapter 2 PDF Overview

RD Sharma Class 10 Chapter 2 PDF helps students learn maths in a simple and quick way. This chapter, called "Polynomials," comes after real numbers and covers some of the most important algebra topics needed for exams and future maths learning.

Main topics in Chapter 2:

• Types of Polynomials: linear, quadratic, cubic, and more
• Degree of a polynomial and how to find it
• Zeros of a polynomial and how to calculate them
• Relationship between coefficients and zeros
• Factorization of polynomials and solving equations
• Graphical meaning of polynomials

The RD Sharma Class 10 Chapter 2 PDF gives step-by-step solutions, easy hints, and simple explanations for all questions. It follows the latest CBSE syllabus Class 10 and is perfect for practice and revision at home. With this PDF, you can check your answers whenever you are confused or stuck. Sometimes, students think polynomials are difficult, but these solutions in the PDF make the chapter much easier.

Why use RD Sharma Class 10 Chapter 2 PDF?

• Every question is solved in a simple and clear way
• Useful for exam preparation and regular homework
• Formulas and important points are explained with proper steps
• You can download and study offline, so no internet needed
• It’s free to access and helpful even if you make mistake during practice

Advantages of Solving RD Sharma Class 10 Chapter 2: Polynomials

• Builds Strong Concepts: Solving RD Sharma Chapter 2 helps you understand key topics like types of polynomials, finding zeros, and relationships of coefficients. These are useful for higher-level maths too.
• Improves Problem-Solving: The chapter has lots of practice problems, including extra and tough ones, helping students build strong problem-solving and thinking skills.
• Board Exam Ready: The practice questions are made as per latest CBSE Board guidelines, helping you get ready for Class 10 Maths board exam.
• Speed and Accuracy: Regular practice with RD Sharma Class 10 Chapter 2 PDF boosts your speed and accuracy, which is very important during exams.
• Full Solutions: Every exercise has detailed solutions, making each step clear so you don’t get confused anywhere.
• Prepares for Competitive Exams: Understanding polynomials is important for competitive exams like JEE Mains and NEET also. Practicing this chapter sets your base for those exams too.

So, use the RD Sharma Class 10 Chapter 2 PDF to make polynomials simple and score well in exams, even if you make some mistake during learning!