The graph does not cut the x-axis but cuts the line y = 2 twice. What is certain about its zeroes?
Answer and explanation
Correct answer: No zero is shown from the given data
The geometrical meaning of a zero is tied specifically to the x-intercept. A number r is a zero of p(x) when p(r) = 0, so the point (r, 0) lies on the graph. The line y = 2 is not the x-axis; every point on it has ordinate 2, not 0. Therefore, its two intersections do not represent zeroes. Since the graph is stated not to cut the x-axis, the supplied information displays no zero. It does not prove that the polynomial has no real zero anywhere unless the whole graph is known, but among the given data, option A is the only certain statement. Options B and C incorrectly treat y = 2 intersections as x-intercepts, while D has no basis.
Frequently asked questions
What is the correct answer to this question?
No zero is shown from the given data
Why is this the correct answer?
The geometrical meaning of a zero is tied specifically to the x-intercept. A number r is a zero of p(x) when p(r) = 0, so the point (r, 0) lies on the graph. The line y = 2 is not the x-axis; every point on it has ordinate 2, not 0. Therefore, its two intersections do not represent zeroes. Since the graph is stated not to cut the x-axis, the supplied information displays no zero. It does not prove that the polynomial has no real zero anywhere unless the whole graph is known, but among the given data, option A is the only certain statement. Options B and C incorrectly treat y = 2 intersections as x-intercepts, while D has no basis.
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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