Zero Polynomial MCQs Quiz | Class 9
This quiz covers Unit II: Algebra for Class IX Mathematics (Code 041). It focuses on the Zero Polynomial, including its meaning, the context of its degree being not defined, and identification. Attempt all 10 questions and download your result PDF.
Understanding the Zero Polynomial
In the study of Polynomials for Class 9 Algebra, the Zero Polynomial is a unique concept that often confuses students. It is defined as the constant polynomial whose coefficients are all equal to zero. It is denoted simply by 0.
Key Characteristics
- Definition: A polynomial \( P(x) = 0 \) is called the zero polynomial.
- Coefficients: All coefficients of the terms in a zero polynomial are 0.
- Value: The value of the zero polynomial is always 0, regardless of the value of the variable \( x \).
- Graph: Geometrically, the graph of the zero polynomial is the x-axis itself (the line y = 0).
Why is the Degree Not Defined?
For any non-zero constant polynomial (like 5 or -7), the degree is 0 because \( 5 = 5x^0 \). However, for the zero polynomial, we can write:
0 = 0x^1 = 0x^2 = 0x^100 …
Since the coefficient is always zero, any power of \( x \) can be associated with it. Because there is no single “highest power” that defines it uniquely, mathematicians state that the degree of the zero polynomial is not defined.
Zeroes of the Zero Polynomial
A “zero of a polynomial” is a value of \( x \) for which the polynomial equals zero. Since \( P(x) = 0 \) for any real number \( x \), every real number is considered a zero of the zero polynomial.
| Feature | Zero Polynomial | Constant Polynomial (Non-Zero) |
|---|---|---|
| Representation | P(x) = 0 | P(x) = c (where c is not 0) |
| Degree | Not Defined | 0 |
| Number of Zeroes | Infinite (Every real number) | None (No real number makes it 0) |
Quick Revision Notes
- Do not confuse the “zero of a polynomial” (a root) with the “zero polynomial” (the function 0).
- If a question asks for the degree of 0, choose “Not Defined”.
- If a question asks for the degree of 7, choose “0”.
- The zero polynomial is the additive identity in the set of polynomials.
Extra Practice Questions
- Q: If p(x) is a zero polynomial, what is p(100)?
A: 0. - Q: Can we say the degree of zero polynomial is 0?
A: No, it is undefined. - Q: How many terms does a zero polynomial have?
A: It is generally considered a monomial (1 term), though its structure is unique. - Q: What is the coefficient of x^5 in the zero polynomial?
A: 0. - Q: Is the polynomial p(x) = 0x + 0 a zero polynomial?
A: Yes.
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