If the x-axis intersections of a graph are (0, 0), (g, 0), and (−g, 0), where g ≠ 0, what is the sum of the zeroes?
Answer and explanation
Correct answer: 0
A zero is the x-coordinate of an x-axis intersection, so the three zeroes represented by the points are 0, g, and −g. Their sum is 0 + g + (−g) = 0, because g and −g are additive opposites and cancel each other. Thus option A is correct. The condition g ≠ 0 only ensures that the symbolic points g and −g are distinct from the origin; it does not change their sum. The expressions g² and −g² are products or signed square expressions, not the required sum, while g alone represents only one of the nonzero zeroes.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
A zero is the x-coordinate of an x-axis intersection, so the three zeroes represented by the points are 0, g, and −g. Their sum is 0 + g + (−g) = 0, because g and −g are additive opposites and cancel each other. Thus option A is correct. The condition g ≠ 0 only ensures that the symbolic points g and −g are distinct from the origin; it does not change their sum. The expressions g² and −g² are products or signed square expressions, not the required sum, while g alone represents only one of the nonzero 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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