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If the x-axis intersection of a polynomial graph is (a, 0), what is the zero?

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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.

Related tags

PolynomialsX-Axis InterceptReal ZeroGeometrical Meaning Of The Zeroes Of A Polynomial.Geometrical Meaning Of The Zeroes Of A PolynomialMathematicsClass 10 Mcq

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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