The graph of a cubic polynomial cuts the x-axis at three distinct points. What is the number of real zeroes?
Answer and explanation
Correct answer: Three
The geometrical meaning of a zero is the x-coordinate of a point where the graph of p(x) meets or crosses the x-axis. On the x-axis, y = 0, so every distinct intersection represents a distinct real solution of p(x) = 0. The graph in the question has three different intersection points; therefore it has three different real zeroes. The fact that the polynomial is cubic is consistent with this result, since a cubic can have at most three real zeroes. Option B and Option C undercount the visible intersections, while Option D would mean that the graph never met the x-axis. Hence Option A is correct.
Frequently asked questions
What is the correct answer to this question?
Three
Why is this the correct answer?
The geometrical meaning of a zero is the x-coordinate of a point where the graph of p(x) meets or crosses the x-axis. On the x-axis, y = 0, so every distinct intersection represents a distinct real solution of p(x) = 0. The graph in the question has three different intersection points; therefore it has three different real zeroes. The fact that the polynomial is cubic is consistent with this result, since a cubic can have at most three real zeroes. Option B and Option C undercount the visible intersections, while Option D would mean that the graph never met the x-axis. Hence Option A is correct.
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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