If p(5) = 0 and p(−2) = 0, at which x-values will the graph cut the x-axis?
Answer and explanation
Correct answer: 5 and −2
The governing concept is the relationship between polynomial zeroes and x-axis intersections. Whenever p(a) = 0, the point (a, 0) belongs to the graph, so x = a is an x-axis intersection. Here p(5) = 0 gives the point (5, 0), and p(−2) = 0 gives the point (−2, 0). Thus the graph cuts the x-axis at x-values 5 and −2, making option A correct. Option B introduces x = 0 without any information about p(0). Option C changes 5 to −5 and −2 to 2, reversing the signs incorrectly. Option D again replaces −2 with 2. The two given function values directly determine the two requested x-values.
Frequently asked questions
What is the correct answer to this question?
5 and −2
Why is this the correct answer?
The governing concept is the relationship between polynomial zeroes and x-axis intersections. Whenever p(a) = 0, the point (a, 0) belongs to the graph, so x = a is an x-axis intersection. Here p(5) = 0 gives the point (5, 0), and p(−2) = 0 gives the point (−2, 0). Thus the graph cuts the x-axis at x-values 5 and −2, making option A correct. Option B introduces x = 0 without any information about p(0). Option C changes 5 to −5 and −2 to 2, reversing the signs incorrectly. Option D again replaces −2 with 2. The two given function values directly determine the two requested x-values.
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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