Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > Value Based Questions: Polynomials
Class 10 Maths Chapter 2 Question Answers - Polynomials
Ques 1: A charity trust decides to build a prayer hall having a carpet area of 300 square metres with its length one metre more than twice its breadth.
(i) Find the length and the breadth of the hall.
(ii) Which mathematical concept is used in the above problem?
(iii) By building a prayer-hall, which value is depicted by the trust?
Sol: (i) Let the breadth of the hall = x metres
∴ Length of the hall
= 2 [Breadth of the hall] + 1 metre
= (2x + 1) metre
∴ Carpet area of the hall= Length × Breadth
= (2x + 1) × x
= 2x2 + x
But the carpet area of the hall = 300 sq. metre
∴ 2x2 + x = 300
⇒ 2x2 + x – 300 = 0
⇒ 2x2 + 25x – 24x – 300 = 0
⇒ x(2x + 25) –12(2x + 25) = 0
⇒ (x – 12) (2x + 25) = 0
⇒ x – 12 = 0
or 2x + 25 = 0
⇒x = 12
or x = - 252
But x = - 252 is not required as the length
or breadth cannot be negative.
∴ x = 12 m and 2x + 1 = (2 × 12) + 1 = 25 m
∴ Breadth of the hall = 12 m
Length of the hall = 25 m
(ii) Quadratic equations
(iii) Enhancing prayer and God fearing feelings.
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FAQs on Class 10 Maths Chapter 2 Question Answers - Polynomials
| 1. What are polynomials and how are they classified? |  |
Ans. Polynomials are algebraic expressions that consist of variables and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents. They are classified based on their degree (the highest power of the variable) and the number of terms. A polynomial can be a monomial (one term), binomial (two terms), trinomial (three terms), or a polynomial with more than three terms.
| 2. How do you add and subtract polynomials? | |
Ans. To add or subtract polynomials, you combine like terms, which are terms that have the same variable raised to the same power. For example, to add \(3x^2 + 2x + 4\) and \(5x^2 + 3x + 1\), you would add the coefficients of like terms: \((3 + 5)x^2 + (2 + 3)x + (4 + 1) = 8x^2 + 5x + 5\).
| 3. What is the importance of the degree of a polynomial? | |
Ans. The degree of a polynomial is important because it determines the polynomial’s behavior, such as its end behavior and the number of possible roots. A polynomial of degree \(n\) can have at most \(n\) roots, and its graph can have at most \(n-1\) turning points. Understanding the degree helps in predicting how the polynomial will behave as the variable approaches positive or negative infinity.
| 4. How can polynomials be factored? | |
Ans. Polynomials can be factored by finding their roots or using methods such as grouping, synthetic division, or applying special formulas (like the difference of squares or perfect square trinomials). For example, the polynomial \(x^2 - 9\) can be factored as \((x - 3)(x + 3)\) using the difference of squares method.
| 5. What are real-world applications of polynomials? | |
Ans. Polynomials have various real-world applications, including in physics for modeling motion, in economics for calculating profit and loss, and in engineering for designing structures. They can represent quantities that change in relation to one another and are used in algorithms for computer graphics, data fitting, and statistical modeling.
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