If the x-axis intersection of a polynomial graph is (a, 0), what is the zero?
Answer and explanation
Correct answer: a
The governing concept is the geometrical meaning of a zero of a polynomial. A number r is a zero of p(x) when p(r) = 0. On a graph, this means that the point (r, 0) lies on the x-axis. Since the stated intersection is (a, 0), substituting its x-coordinate gives p(a) = 0; hence the zero is a. Therefore, option A is the precise answer. The second coordinate, 0, describes the y-coordinate and only confirms that the point lies on the x-axis; it is not the requested zero. Option C simplifies algebraically to a, but option A gives the standard and direct value. Option D changes the sign without any basis.
Frequently asked questions
What is the correct answer to this question?
a
Why is this the correct answer?
The governing concept is the geometrical meaning of a zero of a polynomial. A number r is a zero of p(x) when p(r) = 0. On a graph, this means that the point (r, 0) lies on the x-axis. Since the stated intersection is (a, 0), substituting its x-coordinate gives p(a) = 0; hence the zero is a. Therefore, option A is the precise answer. The second coordinate, 0, describes the y-coordinate and only confirms that the point lies on the x-axis; it is not the requested zero. Option C simplifies algebraically to a, but option A gives the standard and direct value. Option D changes the sign without any 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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