If a polynomial graph has only one x-axis intersection at x = −8, which statement is correct?
Answer and explanation
Correct answer: It has one real zero, −8
A real zero is read from the x-coordinate of an x-axis intersection. The graph has exactly one such intersection, so it has exactly one distinct real zero. Because the intersection occurs at x = −8, the zero is −8, not 8. The minus sign is part of the coordinate and cannot be discarded. Option B confuses the numerical magnitude 8 with the number of zeroes; one intersection does not mean eight zeroes. Option D contradicts the stated intersection. Therefore Option A is correct. This conclusion concerns distinct real zeroes visible on the graph and does not claim anything about possible complex zeroes.
Frequently asked questions
What is the correct answer to this question?
It has one real zero, −8
Why is this the correct answer?
A real zero is read from the x-coordinate of an x-axis intersection. The graph has exactly one such intersection, so it has exactly one distinct real zero. Because the intersection occurs at x = −8, the zero is −8, not 8. The minus sign is part of the coordinate and cannot be discarded. Option B confuses the numerical magnitude 8 with the number of zeroes; one intersection does not mean eight zeroes. Option D contradicts the stated intersection. Therefore Option A is correct. This conclusion concerns distinct real zeroes visible on the graph and does not claim anything about possible complex zeroes.
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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