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Q6. If the graph of a polynomial intersects the x- axis at exactly two points, then which of the following options is correct? A)It cannot be a linear or a cubic polynomial B)It can be a quadratic polynomial only. C)It can be a cubic or a quadratic polynomial. D )It can be a linear or a quadratic polynomial.?
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Q6. If the graph of a polynomial intersects the x- axis at exactly two...
Explanation:
Intersecting the x-axis at exactly two points:
- When a polynomial intersects the x-axis at exactly two points, it means that the graph of the polynomial crosses the x-axis at two distinct points.
- This implies that the polynomial has two real roots.
Determining the degree of the polynomial:
- If a polynomial intersects the x-axis at exactly two points, it must be at least a quadratic polynomial.
- A linear polynomial (degree 1) can intersect the x-axis at only one point, while a cubic polynomial (degree 3) can intersect the x-axis at more than two points.
- Therefore, the polynomial must be of degree 2 or higher.
Options analysis:
- A) It cannot be a linear or a cubic polynomial: This option is correct as a linear polynomial cannot intersect the x-axis at two points, and a cubic polynomial can intersect at more than two points.
- B) It can be a quadratic polynomial only: This option is incorrect as the polynomial could also be of a higher degree.
- C) It can be a cubic or a quadratic polynomial: This option is incorrect as a cubic polynomial can intersect at more than two points.
- D) It can be a linear or a quadratic polynomial: This option is incorrect as a linear polynomial cannot intersect at two points.
Therefore, the correct option is A) It cannot be a linear or a cubic polynomial.
Intersecting the x-axis at exactly two points:
- When a polynomial intersects the x-axis at exactly two points, it means that the graph of the polynomial crosses the x-axis at two distinct points.
- This implies that the polynomial has two real roots.
Determining the degree of the polynomial:
- If a polynomial intersects the x-axis at exactly two points, it must be at least a quadratic polynomial.
- A linear polynomial (degree 1) can intersect the x-axis at only one point, while a cubic polynomial (degree 3) can intersect the x-axis at more than two points.
- Therefore, the polynomial must be of degree 2 or higher.
Options analysis:
- A) It cannot be a linear or a cubic polynomial: This option is correct as a linear polynomial cannot intersect the x-axis at two points, and a cubic polynomial can intersect at more than two points.
- B) It can be a quadratic polynomial only: This option is incorrect as the polynomial could also be of a higher degree.
- C) It can be a cubic or a quadratic polynomial: This option is incorrect as a cubic polynomial can intersect at more than two points.
- D) It can be a linear or a quadratic polynomial: This option is incorrect as a linear polynomial cannot intersect at two points.
Therefore, the correct option is A) It cannot be a linear or a cubic polynomial.
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Q6. If the graph of a polynomial intersects the x- axis at exactly two points, then which of the following options is correct? A)It cannot be a linear or a cubic polynomial B)It can be a quadratic polynomial only. C)It can be a cubic or a quadratic polynomial. D )It can be a linear or a quadratic polynomial.?
Question Description
Q6. If the graph of a polynomial intersects the x- axis at exactly two points, then which of the following options is correct? A)It cannot be a linear or a cubic polynomial B)It can be a quadratic polynomial only. C)It can be a cubic or a quadratic polynomial. D )It can be a linear or a quadratic polynomial.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q6. If the graph of a polynomial intersects the x- axis at exactly two points, then which of the following options is correct? A)It cannot be a linear or a cubic polynomial B)It can be a quadratic polynomial only. C)It can be a cubic or a quadratic polynomial. D )It can be a linear or a quadratic polynomial.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q6. If the graph of a polynomial intersects the x- axis at exactly two points, then which of the following options is correct? A)It cannot be a linear or a cubic polynomial B)It can be a quadratic polynomial only. C)It can be a cubic or a quadratic polynomial. D )It can be a linear or a quadratic polynomial.?.
Q6. If the graph of a polynomial intersects the x- axis at exactly two points, then which of the following options is correct? A)It cannot be a linear or a cubic polynomial B)It can be a quadratic polynomial only. C)It can be a cubic or a quadratic polynomial. D )It can be a linear or a quadratic polynomial.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q6. If the graph of a polynomial intersects the x- axis at exactly two points, then which of the following options is correct? A)It cannot be a linear or a cubic polynomial B)It can be a quadratic polynomial only. C)It can be a cubic or a quadratic polynomial. D )It can be a linear or a quadratic polynomial.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q6. If the graph of a polynomial intersects the x- axis at exactly two points, then which of the following options is correct? A)It cannot be a linear or a cubic polynomial B)It can be a quadratic polynomial only. C)It can be a cubic or a quadratic polynomial. D )It can be a linear or a quadratic polynomial.?.
Solutions for Q6. If the graph of a polynomial intersects the x- axis at exactly two points, then which of the following options is correct? A)It cannot be a linear or a cubic polynomial B)It can be a quadratic polynomial only. C)It can be a cubic or a quadratic polynomial. D )It can be a linear or a quadratic polynomial.? in English & in Hindi are available as part of our courses for UPSC.
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Here you can find the meaning of Q6. If the graph of a polynomial intersects the x- axis at exactly two points, then which of the following options is correct? A)It cannot be a linear or a cubic polynomial B)It can be a quadratic polynomial only. C)It can be a cubic or a quadratic polynomial. D )It can be a linear or a quadratic polynomial.? defined & explained in the simplest way possible. Besides giving the explanation of
Q6. If the graph of a polynomial intersects the x- axis at exactly two points, then which of the following options is correct? A)It cannot be a linear or a cubic polynomial B)It can be a quadratic polynomial only. C)It can be a cubic or a quadratic polynomial. D )It can be a linear or a quadratic polynomial.?, a detailed solution for Q6. If the graph of a polynomial intersects the x- axis at exactly two points, then which of the following options is correct? A)It cannot be a linear or a cubic polynomial B)It can be a quadratic polynomial only. C)It can be a cubic or a quadratic polynomial. D )It can be a linear or a quadratic polynomial.? has been provided alongside types of Q6. If the graph of a polynomial intersects the x- axis at exactly two points, then which of the following options is correct? A)It cannot be a linear or a cubic polynomial B)It can be a quadratic polynomial only. C)It can be a cubic or a quadratic polynomial. D )It can be a linear or a quadratic polynomial.? theory, EduRev gives you an
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