RD Sharma Chapter 6 Class 9 Maths Exercise 6.2 Solutions is about the Factorization of Polynomial in which students will learn about finding the value of a polynomial. In this exercise, we will discuss the- Zeros (roots) of a polynomial, The Value of a polynomial, And some Important theorem. Moreover, students will learn about the tips and tricks to solve the factorization of the polynomial in an easy way.
In the attached PDF, we have given a stepwise explanation for each problem. Students can refer to these questions for practice for the exam. Our experts prepare the list of problems mentioned in the PDF with the help of CBSE and RD Sharma Book after referring to previous year papers of class 9.
Download RD Sharma Chapter 6 Class 9 Maths Exercise 6.2 Solutions PDF
Solutions for Class 9 Maths Chapter 6 Factorization of Polynomials Exercise 6.2
Important Definitions RD Sharma Chapter 6 Class 9 Maths Exercise 6.2 Solutions
The Chapter 6 Class 9 Maths Exercise 6.2, the factorization of polynomials is based on the following topics and subtopics-
- Zeros (roots) of a polynomial.
- Value of a polynomial: The value of a polynomial f(x) at x = a is concerned about replacing x = a in the given polynomial and is indicated by f(a).
- Results of some Important theorem.
Zeros/ Roots of a Polynomial
It is an answer to the polynomial equation, P(x) = 0. It is such a value of x that forms the polynomial equal to 0.
In other terms, the number ‘r’ is a root of a polynomial P(x), if and only if P(r) = 0.
Example-
1. Let P(x) = 5x3 − 4x2 + 7x − 8. Then a root of that polynomial is 1 because according to the definition:
= 5 – 4 + 7 – 8
= 0
It is usual to speak of a root of a polynomial. In general, we say a zero.
2. The roots of the quadratic-
= x2 – x- 6 = (x+2) (x-3)
are −2 and 3. Those are the values of ‘x’ that will give the polynomial equal to 0.
Value of a Polynomial
The value of a polynomial f(x) at x = a is concerned about replacing x = a in the given polynomial and is indicated by f(a).
Example-
7+5-2 is a polynomial is of degree 2 or a quadratic polynomial in.
Examples Based on the Value of Polynomial
Ques- f(x) = 3x + 1, x = −1/3
Solution- f(x) = 3x + 1, x = −1/3
f(x) = 3x + 1
Substitute x = −1/3 in f(x)
f( −1/3) = 3(−1/3) + 1
= -1 + 1
= 0
Since, the result is 0, so x = −1/3 is the root of 3x + 1
Ques 2- g(x) = 3x2 – 2 , x = 2/√3 , −2/√3
Solution- g(x) = 3x2 – 2
Substitute x = 2/√3 in g(x)
g(2/√3) = 3(2/√3)2 – 2
= 3(4/3) – 2
= 4 – 2
= 2 ≠ 0
Now, Substitute x = −2/√3 in g(x)
g(2/√3) = 3(-2/√3)2 – 2
= 3(4/3) – 2
= 4 – 2
= 2 ≠ 0
Since, the results when x = 2/√3 and x = −2/√3) are not 0. Therefore (2/√3 , −2/√3 ) are not zeros of 3x2–2.
Frequently Asked Questions (FAQs) of RD Sharma Chapter 6 Class 9 Maths Exercise 6.2 Solutions
Ques 1- What is the meaning of rationalization?
Ans- Rationalization means organizing something into a logically consistent system.
Ques 2- Can 0 be a polynomial?
Ans- Alike any constant value, the value Zero (0) can be recognized as a (constant) polynomial, called the zero polynomial.
Ques 3- Can zero be a root?
Ans- A root/ zero of a polynomial is the value(s) of X that makes the polynomial to = 0 (or make Y=0). This is an X-intercept. The root is the X-value, and zero (0) is the Y-value.