The graph shows p(2)=0. What is its geometric meaning?
Answer and explanation
Correct answer: The graph meets the x-axis at (2,0)
p(2)=0 means the function value at x=2 is y=p(2)=0, so the point (2,0) lies on the graph — i.e., the graph crosses the x-axis at (2,0). Option B is wrong because the y-axis is at x=0, not x=2. Options C and D are also incorrect: C asserts a vertex at (0,2) without justification, and D implies the graph is a vertical line parallel to x=2, which is not true for a typical polynomial function. Exam tip: p(a)=0 indicates a is a root and corresponds to the x-intercept (a,0) on the graph.
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What is the correct answer to this question?
The graph meets the x-axis at (2,0)
Why is this the correct answer?
p(2)=0 means the function value at x=2 is y=p(2)=0, so the point (2,0) lies on the graph — i.e., the graph crosses the x-axis at (2,0). Option B is wrong because the y-axis is at x=0, not x=2. Options C and D are also incorrect: C asserts a vertex at (0,2) without justification, and D implies the graph is a vertical line parallel to x=2, which is not true for a typical polynomial function. Exam tip: p(a)=0 indicates a is a root and corresponds to the x-intercept (a,0) on the graph.
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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