If the graph of a polynomial goes from above the x-axis to below it and the point (9,0) lies exactly at that crossing, what does (9,0) represent?
Answer and explanation
Correct answer: (x=9) is a zero
The point (9,0) lies on the x-axis, so for the polynomial p(x) we have \(p(9)=0\); hence x=9 is a root (zero). The fact that the graph goes from above to below shows the curve crosses the axis at that point, which indicates a root of odd order (often a simple root). Option B is wrong because y=9 is not implied by a point on the x-axis; option C is wrong because a nonzero constant polynomial does not cross the x-axis; option D contradicts the given point lying on the x-axis. Exam tip: A crossing of the x-axis implies a zero with odd multiplicity; touching-and-returning implies even multiplicity.
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What is the correct answer to this question?
(x=9) is a zero
Why is this the correct answer?
The point (9,0) lies on the x-axis, so for the polynomial p(x) we have \(p(9)=0\); hence x=9 is a root (zero). The fact that the graph goes from above to below shows the curve crosses the axis at that point, which indicates a root of odd order (often a simple root). Option B is wrong because y=9 is not implied by a point on the x-axis; option C is wrong because a nonzero constant polynomial does not cross the x-axis; option D contradicts the given point lying on the x-axis. Exam tip: A crossing of the x-axis implies a zero with odd multiplicity; touching-and-returning implies even multiplicity.
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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