If a graph cuts the x-axis at (2,0) and (8,0), what is the position of x=5 between them?
Answer and explanation
Correct answer: It is the midpoint of the two zeroes
The relevant concept is the midpoint of two numbers on the x-number line. The two x-intercepts have x-coordinates 2 and 8. Their midpoint is calculated by averaging them: (2+8)/2 = 10/2 = 5. Thus x=5 lies exactly halfway between the two given zeroes. This calculation only identifies its position; it does not prove that p(5)=0, because a polynomial may take a nonzero value between its zeroes. Therefore Option A is correct. Option B confuses a midpoint with a zero, Option C refers to a point on the y-axis where x=0, and Option D is false because 8, not 5, is the greater zero.
Frequently asked questions
What is the correct answer to this question?
It is the midpoint of the two zeroes
Why is this the correct answer?
The relevant concept is the midpoint of two numbers on the x-number line. The two x-intercepts have x-coordinates 2 and 8. Their midpoint is calculated by averaging them: (2+8)/2 = 10/2 = 5. Thus x=5 lies exactly halfway between the two given zeroes. This calculation only identifies its position; it does not prove that p(5)=0, because a polynomial may take a nonzero value between its zeroes. Therefore Option A is correct. Option B confuses a midpoint with a zero, Option C refers to a point on the y-axis where x=0, and Option D is false because 8, not 5, is the greater zero.
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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