If the x-axis intersection of a polynomial graph is (a, 0), what is the zero?
Answer and explanation
Correct answer: a
A point on the x-axis has the form (x, 0). If the graph intersects that axis at (a, 0), then substituting its x-coordinate gives p(a) = 0. By definition, a number r is a zero of p(x) when p(r) equals zero, so the zero represented by this intersection is a. The second coordinate, 0, only indicates that the point lies on the x-axis; it is not the zero being asked for. Option C simplifies to a but is unnecessarily written and does not express the standard coordinate rule as clearly. Option D changes the sign without justification. Therefore Option A is the precise answer.
Frequently asked questions
What is the correct answer to this question?
a
Why is this the correct answer?
A point on the x-axis has the form (x, 0). If the graph intersects that axis at (a, 0), then substituting its x-coordinate gives p(a) = 0. By definition, a number r is a zero of p(x) when p(r) equals zero, so the zero represented by this intersection is a. The second coordinate, 0, only indicates that the point lies on the x-axis; it is not the zero being asked for. Option C simplifies to a but is unnecessarily written and does not express the standard coordinate rule as clearly. Option D changes the sign without justification. Therefore Option A is the precise answer.
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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