If a polynomial graph crosses the x-axis three times and touches it once, what is the number of distinct real zeroes?
Answer and explanation
Correct answer: Four
Every point where a polynomial graph meets the x-axis has y-coordinate zero, so its x-coordinate is a real zero of the polynomial. A crossing and a touching are both types of x-axis contact; the difference concerns the behaviour of the graph near the zero, not whether the value is zero. The graph crosses at three points and touches at one more point. Since the question describes these as separate contacts, there are 3 + 1 = 4 distinct x-axis points and therefore four distinct real zeroes. Option B is correct. Counting only crossings gives three and wrongly ignores the touching point; one and zero do not account for the stated contacts.
Frequently asked questions
What is the correct answer to this question?
Four
Why is this the correct answer?
Every point where a polynomial graph meets the x-axis has y-coordinate zero, so its x-coordinate is a real zero of the polynomial. A crossing and a touching are both types of x-axis contact; the difference concerns the behaviour of the graph near the zero, not whether the value is zero. The graph crosses at three points and touches at one more point. Since the question describes these as separate contacts, there are 3 + 1 = 4 distinct x-axis points and therefore four distinct real zeroes. Option B is correct. Counting only crossings gives three and wrongly ignores the touching point; one and zero do not account for the stated contacts.
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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