NCERT Solutions for Class 9 Maths Exercise 2.2 Question 4
Understanding the Question 🧐
To find the zero of a polynomial, we need to find the value of the variable (&&x&&) that makes the entire polynomial equal to 0. The method is simple:
- Set the polynomial expression equal to zero: &&p(x) = 0&&.
- Solve the resulting equation for &&x&&.
The solution for &&x&& is the zero of the polynomial.
Find the zero of the polynomial in each of the following cases:
Solutions 📝
(i) &&p(x) = x + 5&&
Solving for &&x&&, we get &&x = -5&&.
The zero of the polynomial is -5.
(ii) &&p(x) = x – 5&&
Solving for &&x&&, we get &&x = 5&&.
The zero of the polynomial is 5.
(iii) &&p(x) = 2x + 5&&
&&2x = -5&&
&&x = -\frac{5}{2}&&
The zero of the polynomial is &&-\frac{5}{2}&&.
(iv) &&p(x) = 3x – 2&&
&&3x = 2&&
&&x = \frac{2}{3}&&
The zero of the polynomial is &&\frac{2}{3}&&.
(v) &&p(x) = 3x&&
&&x = \frac{0}{3}&&
&&x = 0&&
The zero of the polynomial is 0.
(vi) &&p(x) = ax, a \neq 0&&
Since &&a \neq 0&&, we can divide by &&a&&.
&&x = \frac{0}{a}&&
&&x = 0&&
The zero of the polynomial is 0.
(vii) &&p(x) = cx + d, c \neq 0, c, d&& are real numbers
&&cx = -d&&
&&x = -\frac{d}{c}&&
The zero of the polynomial is &&-\frac{d}{c}&&.
- The zero of a polynomial &&p(x)&& is the solution to the equation &&p(x) = 0&&.
- This value is also known as the root of the equation.
- A linear polynomial of the form &&ax + b&& (where &&a \neq 0&&) will always have exactly one zero, which is &&-\frac{b}{a}&&.
FAQ ❓
Q: What is the first step to find the zero of a polynomial?
A: The first and most important step is to set the polynomial expression equal to zero. If the polynomial is &&p(x)&&, you create the equation &&p(x) = 0&& and then solve for &&x&&.
Q: How is a ‘zero of a polynomial’ different from the number 0?
A: The number 0 is just a value. A “zero of a polynomial” is a specific value of &&x&& that makes the polynomial’s result become 0. For &&p(x) = x – 5&&, the zero is 5. Sometimes, the zero can be the number 0 itself, as in the case of &&p(x) = 3x&&.
Further Reading 📖
To learn more about finding the zeroes 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/.
