A graph crosses the x-axis at x = 1 and x = 4. If p(2) > 0, why is x = 2 not a zero?
Answer and explanation
Correct answer: Because p(2) ≠ 0
The defining condition for x = a to be a zero of p(x) is p(a) = 0. The graph crosses the x-axis at x = 1 and x = 4, so those x-values give zero function values. At x = 2, the question states p(2) > 0. A positive value is not zero, so the point on the graph has a positive y-coordinate and is above the x-axis. Therefore x = 2 is not a zero, and option B is correct. Merely lying between two zeroes does not make a number a zero. The positivity of 2 itself is also irrelevant; what matters is the value p(2).
Frequently asked questions
What is the correct answer to this question?
Because p(2) ≠ 0
Why is this the correct answer?
The defining condition for x = a to be a zero of p(x) is p(a) = 0. The graph crosses the x-axis at x = 1 and x = 4, so those x-values give zero function values. At x = 2, the question states p(2) > 0. A positive value is not zero, so the point on the graph has a positive y-coordinate and is above the x-axis. Therefore x = 2 is not a zero, and option B is correct. Merely lying between two zeroes does not make a number a zero. The positivity of 2 itself is also irrelevant; what matters is the value p(2).
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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