What is the main use of counting x-axis intersections in a polynomial graph?
Answer and explanation
Correct answer: To know the number of real zeroes
The x-axis is the set of points whose y-coordinate is zero. Therefore, when a graph y = p(x) intersects the x-axis, the corresponding x-coordinate satisfies p(x) = 0 and is a real zero. Counting distinct x-axis intersections consequently gives the number of distinct real zeroes visible from the graph. It does not always determine the degree: a polynomial may have a higher degree than the number of real intersections. It also does not immediately give the constant term, which is related to the y-intercept p(0), not the x-intercepts. Colour has no mathematical role here. Thus Option A states the correct use.
Frequently asked questions
What is the correct answer to this question?
To know the number of real zeroes
Why is this the correct answer?
The x-axis is the set of points whose y-coordinate is zero. Therefore, when a graph y = p(x) intersects the x-axis, the corresponding x-coordinate satisfies p(x) = 0 and is a real zero. Counting distinct x-axis intersections consequently gives the number of distinct real zeroes visible from the graph. It does not always determine the degree: a polynomial may have a higher degree than the number of real intersections. It also does not immediately give the constant term, which is related to the y-intercept p(0), not the x-intercepts. Colour has no mathematical role here. Thus Option A states the correct use.
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..
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
