If p(0) = -3, which conclusion about the graph is correct?
Answer and explanation
Correct answer: The graph passes through (0, -3)
The value p(0) gives the y-intercept of the polynomial's graph. p(0) = -3 means the graph passes through the point (0, -3). x = 0 would be a root only if p(0) = 0, which is not the case here, so B is wrong. The graph crosses the x-axis at x = -3 only if p(-3) = 0, which we are not told, so C is incorrect. Also p(0) ≠ 0 does not imply there are no zeros at all, so D is false. Exam tip: to test whether x = a is a root compute p(a); to get the y-intercept evaluate p(0).
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What is the correct answer to this question?
The graph passes through (0, -3)
Why is this the correct answer?
The value p(0) gives the y-intercept of the polynomial's graph. p(0) = -3 means the graph passes through the point (0, -3). x = 0 would be a root only if p(0) = 0, which is not the case here, so B is wrong. The graph crosses the x-axis at x = -3 only if p(-3) = 0, which we are not told, so C is incorrect. Also p(0) ≠ 0 does not imply there are no zeros at all, so D is false. Exam tip: to test whether x = a is a root compute p(a); to get the y-intercept evaluate p(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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