The graph cuts the x-axis at (−2, 0), (0, 0), and (5, 0). Which statement is correct?
Answer and explanation
Correct answer: The zeroes are −2, 0, and 5.
Every x-axis intersection has y-coordinate zero, and its x-coordinate is a zero of the polynomial. The three given intersections therefore correspond to x = −2, x = 0, and x = 5. Hence the zeroes are −2, 0, and 5, making option A correct. The origin (0, 0) is itself on the x-axis, so x = 0 must be included; it is not excluded merely because it is the origin. Option B omits a valid zero, option C contradicts the definition of a zero, and option D incorrectly counts only the two nonzero intercepts. The three distinct intersections indicate three distinct real zeroes.
Frequently asked questions
What is the correct answer to this question?
The zeroes are −2, 0, and 5.
Why is this the correct answer?
Every x-axis intersection has y-coordinate zero, and its x-coordinate is a zero of the polynomial. The three given intersections therefore correspond to x = −2, x = 0, and x = 5. Hence the zeroes are −2, 0, and 5, making option A correct. The origin (0, 0) is itself on the x-axis, so x = 0 must be included; it is not excluded merely because it is the origin. Option B omits a valid zero, option C contradicts the definition of a zero, and option D incorrectly counts only the two nonzero intercepts. The three distinct intersections indicate three distinct real zeroes.
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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