Zeros of a Polynomial MCQs Quiz | Class 9
Test your understanding of Algebra Unit II for Class IX Mathematics (Code 041). This quiz covers the definition of zeros (roots), finding zeros of linear and quadratic polynomials, and the relationship between roots and factors (x-a). Submit your answers to see your score and download the detailed solution PDF.
Understanding Zeros of a Polynomial
In Class 9 Mathematics, the concept of the “zero” of a polynomial is fundamental to Algebra. A zero (or root) of a polynomial p(x) is a specific value of x, let’s call it ‘c’, such that p(c) = 0.
For example, if p(x) = x – 2, then putting x = 2 gives p(2) = 2 – 2 = 0. Therefore, 2 is a zero of the polynomial x – 2.
Key Concepts & Formulas
- Linear Polynomial (ax + b): Has exactly one zero. The zero is calculated as x = -b/a.
- Quadratic Polynomial (ax^2 + bx + c): Can have at most two zeros.
- Zero Polynomial: The constant polynomial 0 has every real number as its zero.
- Factor Theorem Relation: If ‘a’ is a zero of polynomial p(x), then (x – a) is a factor of p(x). Conversely, if (x – a) is a factor, then p(a) = 0.
Finding the Zero
To find the zero of a polynomial p(x), simply set the polynomial equal to zero and solve for x.
Solution: Set p(x) = 0.
2x + 1 = 0
2x = -1
x = -1/2.
So, -1/2 is the zero.
Summary Table
| Type of Polynomial | Standard Form | Max Number of Zeros |
|---|---|---|
| Linear | ax + b | 1 |
| Quadratic | ax^2 + bx + c | 2 |
| Cubic | ax^3 + bx^2 + cx + d | 3 |
Extra Practice Questions
- Check if x = -1 is a zero of p(x) = x + 1. (Ans: Yes)
- Find the zero of p(x) = 3x – 2. (Ans: 2/3)
- If p(x) = x^2 – 1, what is p(1)? (Ans: 0)
- Find the value of k if x = 1 is a zero of x^2 + kx + 2. (Ans: -3)
- Is 0 a zero of the polynomial p(x) = 2x? (Ans: Yes)
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