NCERT Solutions for Class 9 Maths Exercise 2.1 Question 4
Understanding the Question 🧐
This question asks for the degree of a few polynomials. The degree is a simple but important concept: it’s the highest power (or exponent) of the variable in the polynomial. To find it, we just need to look at all the terms and pick the largest exponent.
Write the degree of each of the following polynomials:
(i) &&5x^3 + 4x^2 + 7x&&
(ii) &&4 – y^2&&
(iii) &&5t – \sqrt{7}&&
(iv) &&3&&
Part (i): &&5x^3 + 4x^2 + 7x&& 📝
Step 1: Identify the power of the variable in each term.
- In the term &&5x^3&&, the power of &&x&& is 3.
- In the term &&4x^2&&, the power of &&x&& is 2.
- In the term &&7x&& (which is &&7x^1&&), the power of &&x&& is 1.
Step 2: Find the highest power among them.
The powers are {3, 2, 1}. The highest value is 3.
Conclusion: The degree of the polynomial is 3.
Part (ii): &&4 – y^2&& 📝
Step 1: Identify the power of the variable in each term.
- In the term &&-y^2&&, the power of &&y&& is 2.
- The term &&4&& is a constant. We can write it as &&4y^0&&, so the power of &&y&& is 0.
Step 2: Find the highest power among them.
The powers are {2, 0}. The highest value is 2.
Conclusion: The degree of the polynomial is 2.
Part (iii): &&5t – \sqrt{7}&& 📝
Step 1: Identify the power of the variable in each term.
- In the term &&5t&& (which is &&5t^1&&), the power of &&t&& is 1.
- The term &&-\sqrt{7}&& is a constant, which can be written as &&-\sqrt{7}t^0&&. The power of &&t&& is 0.
Step 2: Find the highest power among them.
The powers are {1, 0}. The highest value is 1.
Conclusion: The degree of the polynomial is 1.
Part (iv): &&3&& 📝
Step 1: Identify the type of polynomial.
The number &&3&& is a non-zero constant polynomial.
Step 2: Identify the power of the variable.
A constant can always be written with a variable raised to the power of 0. For example, &&3 = 3x^0&& (since &&x^0=1&&).
Therefore, the highest (and only) power of the variable is 0.
Conclusion: The degree of the polynomial is 0.
- The degree is the largest exponent of the variable.
- A variable with no visible exponent (like &&x&&) has a degree of 1.
- A non-zero constant (like 5, -10, etc.) has a degree of 0.
- The degree classifies polynomials: degree 1 is linear, degree 2 is quadratic, and degree 3 is cubic.
FAQ ❓
Q: What is the degree of a polynomial?
A: The degree of a polynomial is the highest power (exponent) of the variable in any of its terms. For example, in &&2x^4 + x^2&&, the powers are 4 and 2, so the degree is 4.
Q: What is the degree of a constant number like 3?
A: The degree of any non-zero constant number is 0. This is because a constant like 3 can be written as &&3 \times x^0&&, and the power of the variable is 0.
Q: Does the coefficient (like &&\sqrt{7}&&) affect the degree?
A: No, the coefficient does not affect the degree. The degree is determined only by the exponent of the variable. In the term &&5t – \sqrt{7}&&, the degree is 1 because of the ‘&&t&&’ term, regardless of the constant &&\sqrt{7}&&.
Further Reading 📖
To learn more about the degree of polynomials, 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/.
