If the points meeting the x-axis are written as (2,0), (2,0), (9,0), how many distinct real zeroes are there?
Answer and explanation
Correct answer: Two
The governing concept is the geometrical meaning of a zero: the x-coordinate of a point where the polynomial graph meets the x-axis. The listed x-coordinates are 2, 2 and 9. The repeated point (2,0) represents the same x-value twice, so it contributes only one distinct real zero. The other distinct x-value is 9. Thus the set of distinct zeroes is {2,9}, containing two elements, and Option B is correct. Option A ignores 9, while Option C counts the repeated coordinate twice rather than counting distinct values. Option D is not supported because only two different x-coordinates have been given.
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What is the correct answer to this question?
Two
Why is this the correct answer?
The governing concept is the geometrical meaning of a zero: the x-coordinate of a point where the polynomial graph meets the x-axis. The listed x-coordinates are 2, 2 and 9. The repeated point (2,0) represents the same x-value twice, so it contributes only one distinct real zero. The other distinct x-value is 9. Thus the set of distinct zeroes is {2,9}, containing two elements, and Option B is correct. Option A ignores 9, while Option C counts the repeated coordinate twice rather than counting distinct values. Option D is not supported because only two different x-coordinates have been given.
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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