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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
But 
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? |  |
Ans. Polynomials are mathematical expressions that consist of variables, coefficients, and exponents. They are made up of terms, which are either constants or variables raised to a power. Examples of polynomials include 2x^2 + 3x + 1 and 4y^3 - 2y + 5.
| 2. How do you classify polynomials based on their degree? | |
Ans. Polynomials can be classified based on their degree, which is determined by the highest exponent of the variable present in the polynomial. For example, if the highest exponent is 2, then the polynomial is a quadratic polynomial. If the highest exponent is 3, then it is a cubic polynomial. Similarly, if the highest exponent is 1, it is a linear polynomial.
| 3. What is the zero of a polynomial? | |
Ans. The zero of a polynomial is the value of the variable that makes the polynomial equal to zero. In other words, it is the solution to the equation formed by setting the polynomial equal to zero. The zeros of a polynomial are also known as the roots or x-intercepts of the polynomial.
| 4. How do you add and subtract polynomials? | |
Ans. To add or subtract polynomials, you need to combine the like terms. Like terms are terms that have the same variable and the same exponent. For addition, simply add the coefficients of the like terms. For subtraction, change the sign of the terms being subtracted and then add the coefficients of the like terms.
| 5. Can a polynomial have more than one variable? | |
Ans. Yes, a polynomial can have more than one variable. These types of polynomials are called multivariable polynomials. In multivariable polynomials, each term can have different variables with different exponents. Examples of multivariable polynomials include 3xy^2 + 2x^2y - 5xyz and 4x^2y^2z + 2xy^3z^2 - 6xyz.
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