If the points meeting the x-axis on a polynomial graph are written as (1,0), (1,0), (4,0), how many distinct real zeroes are there?
Answer and explanation
Correct answer: Two
The governing concept is that a real zero of a polynomial is an x-coordinate at which its graph meets the x-axis. The listed points have x-coordinates 1, 1, and 4. Although the point (1,0) appears twice, repetition does not create a new distinct zero; it only indicates that the same zero may have repeated multiplicity. Therefore the distinct x-values are 1 and 4, giving exactly two distinct real zeroes. Option A is incorrect because there are two different x-values, while Option C incorrectly counts the repeated listing separately. Option D has no basis in the data.
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What is the correct answer to this question?
Two
Why is this the correct answer?
The governing concept is that a real zero of a polynomial is an x-coordinate at which its graph meets the x-axis. The listed points have x-coordinates 1, 1, and 4. Although the point (1,0) appears twice, repetition does not create a new distinct zero; it only indicates that the same zero may have repeated multiplicity. Therefore the distinct x-values are 1 and 4, giving exactly two distinct real zeroes. Option A is incorrect because there are two different x-values, while Option C incorrectly counts the repeated listing separately. Option D has no basis in the data.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Geometrical meaning of the zeroes of a polynomial..
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