NCERT Solutions for Class 9 Maths Exercise 2.2 Question 1
Understanding the Question 🧐
This question asks us to find the value of a given polynomial for three different values of the variable &&x&&. To do this, we simply need to substitute the given value into the polynomial expression wherever we see ‘&&x&&’ and then calculate the result.
Find the value of the polynomial &&5x – 4x^2 + 3&& at:
(i) &&x = 0&&
(ii) &&x = -1&&
(iii) &&x = 2&&
Let’s name our polynomial &&p(x) = 5x – 4x^2 + 3&& for easier notation.
Part (i): Value at &&x = 0&& 📝
Step 1: Substitute &&x = 0&& into the polynomial &&p(x)&&.
&&p(0) = 5(0) – 4(0)^2 + 3&&
Step 2: Calculate the result.
&&p(0) = 0 – 4(0) + 3&&
&&p(0) = 0 – 0 + 3&&
&&p(0) = 3&&
Conclusion: The value of the polynomial at &&x = 0&& is 3.
Part (ii): Value at &&x = -1&& 📝
Step 1: Substitute &&x = -1&& into the polynomial. Use parentheses to avoid sign errors.
&&p(-1) = 5(-1) – 4(-1)^2 + 3&&
Step 2: Calculate the result, remembering that &&(-1)^2 = 1&&.
&&p(-1) = -5 – 4(1) + 3&&
&&p(-1) = -5 – 4 + 3&&
&&p(-1) = -9 + 3&&
&&p(-1) = -6&&
Conclusion: The value of the polynomial at &&x = -1&& is -6.
Part (iii): Value at &&x = 2&& 📝
Step 1: Substitute &&x = 2&& into the polynomial.
&&p(2) = 5(2) – 4(2)^2 + 3&&
Step 2: Calculate the result, remembering that &&2^2 = 4&&.
&&p(2) = 10 – 4(4) + 3&&
&&p(2) = 10 – 16 + 3&&
&&p(2) = -6 + 3&&
&&p(2) = -3&&
Conclusion: The value of the polynomial at &&x = 2&& is -3.
- To find the value of a polynomial &&p(x)&& at &&x=a&&, you calculate &&p(a)&&.
- Always follow the order of operations (BODMAS/PEMDAS): evaluate powers/exponents first, then multiplication, and finally addition/subtraction.
- Pay close attention to positive and negative signs.
FAQ ❓
Q: What does &&p(x)&& notation mean?
A: The notation &&p(x)&& is a way to name a polynomial. ‘p’ is the name, and ‘(x)’ indicates that ‘&&x&&’ is the variable. For example, &&p(x) = 5x – 4x^2 + 3&&. Finding &&p(0)&& is shorthand for “find the value of polynomial p when &&x = 0&&”.
Q: What is the most common mistake when substituting negative values?
A: The most common mistake is mishandling the sign when squaring a negative number. For instance, when substituting &&x = -1&& into &&-4x^2&&, the correct calculation is &&-4(-1)^2 = -4(1) = -4&&. A common error is to multiply &&-4&& and &&-1&& first, which is incorrect.
Further Reading 📖
To learn more about finding the value 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/.
