NCERT Solutions for Class 9 Maths Exercise 2.1 Question 2
Understanding the Question 🧐
This question asks us to find the coefficient of the &&x^2&& term in a few different polynomials. A coefficient is simply the number that is multiplied by a variable. Our task is to locate the &&x^2&& term in each expression and identify the number attached to it.
Write the coefficients of &&x^2&& in each of the following:
(i) &&2 + x^2 + x&&
(ii) &&2 – x^2 + x^3&&
(iii) &&\frac{\pi}{2}x^2 + x&&
(iv) &&\sqrt{2}x – 1&&
Part (i): &&2 + x^2 + x&& 📝
Step 1: Locate the &&x^2&& term.
In the expression &&2 + x^2 + x&&, the term containing &&x^2&& is simply &&x^2&&.
Step 2: Identify the numerical factor.
When no number is written in front of a variable, it is understood to be 1. So, &&x^2&& is the same as &&1 \times x^2&&.
Conclusion: The coefficient of &&x^2&& is 1.
Part (ii): &&2 – x^2 + x^3&& 📝
Step 1: Locate the &&x^2&& term.
In the expression &&2 – x^2 + x^3&&, the term with &&x^2&& is &&-x^2&&. Remember to include the sign!
Step 2: Identify the numerical factor.
The term &&-x^2&& is the same as &&-1 \times x^2&&.
Conclusion: The coefficient of &&x^2&& is -1.
Part (iii): &&\frac{\pi}{2}x^2 + x&& 📝
Step 1: Locate the &&x^2&& term.
The term containing &&x^2&& is &&\frac{\pi}{2}x^2&&.
Step 2: Identify the numerical factor.
The number being multiplied by &&x^2&& is &&\frac{\pi}{2}&&.
Conclusion: The coefficient of &&x^2&& is &&\frac{\pi}{2}&&.
Part (iv): &&\sqrt{2}x – 1&& 📝
Step 1: Locate the &&x^2&& term.
In the expression &&\sqrt{2}x – 1&&, there is no term containing &&x^2&&.
Step 2: Identify the numerical factor.
When a term is missing from a polynomial, its coefficient is considered to be 0. We can imagine the term &&0x^2&& being part of the expression.
Conclusion: The coefficient of &&x^2&& is 0.
- The coefficient is the number multiplied by the variable term.
- Always include the sign (&&+&& or &&-&&) with the coefficient.
- If no number is shown, the coefficient is 1 (for &&+x^2&&) or -1 (for &&-x^2&&).
- If the term does not exist in the polynomial, its coefficient is 0.
FAQ ❓
Q: What is a coefficient in a polynomial?
A: A coefficient is the numerical factor that is multiplied by a variable in a term of a polynomial. For example, in the term &&5x^2&&, the coefficient of &&x^2&& is 5.
Q: Why is the coefficient of &&x^2&& in &&2 – x^2 + x^3&& equal to -1?
A: The term with &&x^2&& is &&-x^2&&. This can be written as &&-1 \times x^2&&. Therefore, the coefficient is -1. The sign is always included with the coefficient.
Q: Why is the coefficient of &&x^2&& in &&\sqrt{2}x – 1&& equal to 0?
A: The expression &&\sqrt{2}x – 1&& does not contain an &&x^2&& term. When a term is absent from a polynomial, its coefficient is considered to be 0. We can think of the expression as &&0x^2 + \sqrt{2}x – 1&&.
Further Reading 📖
To learn more about polynomials and their terms, you can refer to the official NCERT textbook for Class 9 Maths, Chapter 2. More resources are available on the NCERT website at https://ncert.nic.in/.
