For a polynomial, p(1) = 0, p(2) = 0, and p(3) = 0. If these are three distinct zeroes, at how many distinct points will the graph meet the x-axis?
Answer and explanation
Correct answer: Three
A zero of a polynomial is an x-value for which the polynomial value is zero. Geometrically, when p(a) = 0, the graph contains the point (a, 0), which lies on the x-axis. Since p(1) = 0, p(2) = 0, and p(3) = 0, the graph contains (1, 0), (2, 0), and (3, 0). The statement that the zeroes are distinct ensures that these are three different x-axis points. Hence option C, Three, is correct. Two is too small, six counts values and coordinates unnecessarily, and one ignores the other two zeroes.
Frequently asked questions
What is the correct answer to this question?
Three
Why is this the correct answer?
A zero of a polynomial is an x-value for which the polynomial value is zero. Geometrically, when p(a) = 0, the graph contains the point (a, 0), which lies on the x-axis. Since p(1) = 0, p(2) = 0, and p(3) = 0, the graph contains (1, 0), (2, 0), and (3, 0). The statement that the zeroes are distinct ensures that these are three different x-axis points. Hence option C, Three, is correct. Two is too small, six counts values and coordinates unnecessarily, and one ignores the other two zeroes.
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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