Understanding Linear Polynomials
A linear polynomial is a polynomial of degree 1, which can be expressed in the standard form:
- P(x) = ax + b
Where:
- a and b are constants.
- a ≠ 0 (to ensure it is linear).
Finding the Zeros of Linear Polynomials
The zeros (or roots) of a polynomial are the values of x that make the polynomial equal to zero.
- To find the zero of a linear polynomial, set P(x) to zero:
- ax + b = 0
- Rearranging gives us:
- x = -b/a
Key Points on Zeros of Linear Polynomials
- Single Zero: A linear polynomial has exactly one zero because it is a straight line.
- Graph Interpretation: The graph of a linear polynomial intersects the x-axis at one point, which represents the zero.
- Unique Solution: Since the equation ax + b = 0 has only one solution for x (given a ≠ 0), a linear polynomial has one unique zero.
Conclusion
Thus, the correct answer is option 'B': A linear polynomial has 1 zero. This fundamental property distinguishes linear polynomials from higher-degree polynomials, which may have multiple zeros. Understanding this concept is essential for further studies in algebra and polynomial functions.