If p(−6) = 0, p(0) = 0, and p(5) = 0, which statement about the graph is correct?
Answer and explanation
Correct answer: The graph will pass through (−6, 0), (0, 0), and (5, 0)
The governing concept is the coordinate form of a function graph: every input a is represented by the point (a, p(a)). If p(a) = 0, that point becomes (a, 0), which lies on the x-axis and shows that a is a zero. Applying this rule gives p(−6) = 0 → (−6, 0), p(0) = 0 → (0, 0), and p(5) = 0 → (5, 0). Therefore option A is correct. Option B places the given inputs in the second coordinate and incorrectly treats them as y-values. Option C contradicts the three stated zeroes, while option D ignores −6 and 0. The statements establish at least these three x-axis points, whether or not additional zeroes exist.
Frequently asked questions
What is the correct answer to this question?
The graph will pass through (−6, 0), (0, 0), and (5, 0)
Why is this the correct answer?
The governing concept is the coordinate form of a function graph: every input a is represented by the point (a, p(a)). If p(a) = 0, that point becomes (a, 0), which lies on the x-axis and shows that a is a zero. Applying this rule gives p(−6) = 0 → (−6, 0), p(0) = 0 → (0, 0), and p(5) = 0 → (5, 0). Therefore option A is correct. Option B places the given inputs in the second coordinate and incorrectly treats them as y-values. Option C contradicts the three stated zeroes, while option D ignores −6 and 0. The statements establish at least these three x-axis points, whether or not additional zeroes exist.
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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