The graph of a polynomial intersects the y-axis at the point (0, −8). Which conclusion about the polynomial's zeros is correct?
Answer and explanation
Correct answer: A zero cannot be determined from this information alone
The y-intercept gives the value \(p(0)\); here \(p(0)=−8\). Zeros are x-values satisfying \(p(x)=0\), i.e. where the graph meets the x-axis. Knowing only the y-intercept does not determine any x-zero because the y-value (−8) is not an x-coordinate. Option B (zero = −8) is a common confusion that mistakes the y-value for an x-value and is therefore incorrect. Exam tip: to find zeros set \(p(x)=0\) or look for x-axis intersections (y=0).
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What is the correct answer to this question?
A zero cannot be determined from this information alone
Why is this the correct answer?
The y-intercept gives the value \(p(0)\); here \(p(0)=−8\). Zeros are x-values satisfying \(p(x)=0\), i.e. where the graph meets the x-axis. Knowing only the y-intercept does not determine any x-zero because the y-value (−8) is not an x-coordinate. Option B (zero = −8) is a common confusion that mistakes the y-value for an x-value and is therefore incorrect. Exam tip: to find zeros set \(p(x)=0\) or look for x-axis intersections (y=0).
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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