If the y-axis intercept of a graph is (0, 0), what additional conclusion is correct?
Answer and explanation
Correct answer: 0 is also a zero
The governing concept is the relationship between an intercept and a polynomial value. The y-axis intercept is obtained by putting x = 0, so a graph passing through (0, 0) means p(0) = 0. By definition, this makes 0 a zero of the polynomial. The same point is also on the x-axis, because every point with y-coordinate 0 lies on that axis; therefore it is an x-axis intersection as well. Hence option A is correct. The conclusion does not say that every number is a zero, since only x = 0 has been established. It also cannot imply that there is no zero or that only 1 is a zero. Other zeroes may exist, but they cannot be determined from this single intercept alone.
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What is the correct answer to this question?
0 is also a zero
Why is this the correct answer?
The governing concept is the relationship between an intercept and a polynomial value. The y-axis intercept is obtained by putting x = 0, so a graph passing through (0, 0) means p(0) = 0. By definition, this makes 0 a zero of the polynomial. The same point is also on the x-axis, because every point with y-coordinate 0 lies on that axis; therefore it is an x-axis intersection as well. Hence option A is correct. The conclusion does not say that every number is a zero, since only x = 0 has been established. It also cannot imply that there is no zero or that only 1 is a zero. Other zeroes may exist, but they cannot be determined from this single intercept alone.
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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