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Zeroes of a polynomial p(y) is of the p...

Zeroes of a polynomial p(y) is ______ of the point , wherethe grapth intersects the y - axis .

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To solve the question, we need to understand the relationship between the zeroes of a polynomial and the points where its graph intersects the y-axis. ### Step-by-Step Solution: 1. **Understand the Polynomial**: A polynomial \( P(y) \) is a mathematical expression that can be represented in the form of \( a_n y^n + a_{n-1} y^{n-1} + ... + a_1 y + a_0 \), where \( a_n, a_{n-1}, ..., a_0 \) are constants and \( n \) is a non-negative integer. **Hint**: A polynomial is made up of terms with variables raised to whole number powers. 2. **Identify Zeroes of the Polynomial**: The zeroes of a polynomial are the values of \( y \) for which \( P(y) = 0 \). These are the points where the graph of the polynomial intersects the y-axis. **Hint**: To find zeroes, set the polynomial equal to zero and solve for \( y \). 3. **Graph Intersection with the Y-Axis**: The graph of a polynomial intersects the y-axis at points where \( x = 0 \). To find these points, we evaluate \( P(0) \). **Hint**: The y-intercept of a graph occurs when the input variable (in this case, \( y \)) is zero. 4. **Count the Intersection Points**: The number of zeroes of the polynomial \( P(y) \) corresponds to the number of times the graph intersects the y-axis. Each intersection point represents a zero of the polynomial. **Hint**: Each intersection point on the y-axis indicates a solution to \( P(y) = 0 \). 5. **Conclusion**: Therefore, we can conclude that the zeroes of the polynomial \( P(y) \) are the number of points where the graph intersects the y-axis. **Final Answer**: The zeroes of a polynomial \( P(y) \) is **the number of points** where the graph intersects the y-axis.
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