A polynomial graph cuts the x-axis at x = −5 and x = 5. What does this indicate with respect to the y-axis?
Answer and explanation
Correct answer: The zeroes are equally distant from the y-axis
The y-axis is the vertical line x = 0. The distance of a point (x, 0) from the y-axis is the absolute value |x|. For the two x-axis intersections, the distances are |−5| = 5 and |5| = 5. Thus the zeroes correspond to points equally far from the y-axis, one on each side of it: (−5, 0) lies to the left and (5, 0) lies to the right. Therefore option B is correct. They are not on the y-axis because their x-coordinates are not zero. The signs show opposite sides, not that both points lie on one side.
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What is the correct answer to this question?
The zeroes are equally distant from the y-axis
Why is this the correct answer?
The y-axis is the vertical line x = 0. The distance of a point (x, 0) from the y-axis is the absolute value |x|. For the two x-axis intersections, the distances are |−5| = 5 and |5| = 5. Thus the zeroes correspond to points equally far from the y-axis, one on each side of it: (−5, 0) lies to the left and (5, 0) lies to the right. Therefore option B is correct. They are not on the y-axis because their x-coordinates are not zero. The signs show opposite sides, not that both points lie on one side.
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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