The graph of a polynomial meets the x-axis at (a, 0) and (−a, 0). If a ≠ 0, what is the sum of its zeros?
Answer and explanation
Correct answer: 0
Zeros (roots) are the x-coordinates where the graph meets the x-axis, here they are \(a\) and \(-a\). Their sum is \(a + (-a) = 0\). The nearest distractor \(2a\) is wrong because it corresponds to adding magnitudes \(a + a\), not \(a + (-a)\). Exam tip: when roots are opposites (symmetric about origin), their sum is always 0 — spot symmetry to answer quickly.
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What is the correct answer to this question?
0
Why is this the correct answer?
Zeros (roots) are the x-coordinates where the graph meets the x-axis, here they are \(a\) and \(-a\). Their sum is \(a + (-a) = 0\). The nearest distractor \(2a\) is wrong because it corresponds to adding magnitudes \(a + a\), not \(a + (-a)\). Exam tip: when roots are opposites (symmetric about origin), their sum is always 0 — spot symmetry to answer quickly.
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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