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Assertion: The graph y=f(x) is shown in figure, for the polynomial f(x). The number of zeroes of f(x) is 3.
Reason: The number of zero of the polynomial f(x) is the number of point of which f(x) cuts or touches the axes.?
Reason: The number of zero of the polynomial f(x) is the number of point of which f(x) cuts or touches the axes.?
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Assertion: The graph y=f(x) is shown in figure, for the polynomial f(x...
Assertion Explanation
The assertion states that the graph of the polynomial f(x) has three zeroes. A zero of a polynomial is defined as a point where the graph intersects or touches the x-axis.
Understanding Zeroes of a Polynomial
- A zero occurs when f(x) = 0.
- Each intersection point with the x-axis indicates a zero.
- If the graph touches the x-axis without crossing it (i.e., at a point of tangency), it still counts as a zero but typically has a multiplicity greater than one.
Reasoning Behind the Number of Zeroes
- To determine the number of zeroes, observe how many times the graph intersects the x-axis.
- The assertion claims there are three zeroes, implying there are three distinct points where f(x) = 0.
Graph Behavior and Polynomial Degree
- A polynomial of degree n can have at most n zeroes.
- If the polynomial is shown to have three zeroes, it must be at least a degree 3 polynomial.
- The behavior near the zeroes (crossing or touching) provides insights into the multiplicity of each zero.
Conclusion
- The assertion and reason are consistent. The number of zeroes of a polynomial is accurately represented by the number of times the graph intersects or touches the x-axis.
- If the graph indeed shows three such points, the assertion stands confirmed, and the reasoning is valid.
This understanding is crucial for analyzing polynomial functions and their graphical representations in mathematics.
The assertion states that the graph of the polynomial f(x) has three zeroes. A zero of a polynomial is defined as a point where the graph intersects or touches the x-axis.
Understanding Zeroes of a Polynomial
- A zero occurs when f(x) = 0.
- Each intersection point with the x-axis indicates a zero.
- If the graph touches the x-axis without crossing it (i.e., at a point of tangency), it still counts as a zero but typically has a multiplicity greater than one.
Reasoning Behind the Number of Zeroes
- To determine the number of zeroes, observe how many times the graph intersects the x-axis.
- The assertion claims there are three zeroes, implying there are three distinct points where f(x) = 0.
Graph Behavior and Polynomial Degree
- A polynomial of degree n can have at most n zeroes.
- If the polynomial is shown to have three zeroes, it must be at least a degree 3 polynomial.
- The behavior near the zeroes (crossing or touching) provides insights into the multiplicity of each zero.
Conclusion
- The assertion and reason are consistent. The number of zeroes of a polynomial is accurately represented by the number of times the graph intersects or touches the x-axis.
- If the graph indeed shows three such points, the assertion stands confirmed, and the reasoning is valid.
This understanding is crucial for analyzing polynomial functions and their graphical representations in mathematics.
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Assertion: The graph y=f(x) is shown in figure, for the polynomial f(x). The number of zeroes of f(x) is 3.Reason: The number of zero of the polynomial f(x) is the number of point of which f(x) cuts or touches the axes.?
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Assertion: The graph y=f(x) is shown in figure, for the polynomial f(x). The number of zeroes of f(x) is 3.Reason: The number of zero of the polynomial f(x) is the number of point of which f(x) cuts or touches the axes.? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Assertion: The graph y=f(x) is shown in figure, for the polynomial f(x). The number of zeroes of f(x) is 3.Reason: The number of zero of the polynomial f(x) is the number of point of which f(x) cuts or touches the axes.? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion: The graph y=f(x) is shown in figure, for the polynomial f(x). The number of zeroes of f(x) is 3.Reason: The number of zero of the polynomial f(x) is the number of point of which f(x) cuts or touches the axes.?.
Assertion: The graph y=f(x) is shown in figure, for the polynomial f(x). The number of zeroes of f(x) is 3.Reason: The number of zero of the polynomial f(x) is the number of point of which f(x) cuts or touches the axes.? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Assertion: The graph y=f(x) is shown in figure, for the polynomial f(x). The number of zeroes of f(x) is 3.Reason: The number of zero of the polynomial f(x) is the number of point of which f(x) cuts or touches the axes.? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion: The graph y=f(x) is shown in figure, for the polynomial f(x). The number of zeroes of f(x) is 3.Reason: The number of zero of the polynomial f(x) is the number of point of which f(x) cuts or touches the axes.?.
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