A graph cuts the x-axis at (a, 0), (0, 0) and (-a, 0) where \(a \neq 0\). What is the sum of the zeroes?
Answer and explanation
Correct answer: \(0\)
The x-intercepts are the polynomial's zeroes, here \(a,\;0,\;-a\). Their sum is \(a+0+(-a)=0\). The distractor \(2a\) might come from adding absolute values incorrectly; \(-a\) is only one root, not the sum. Exam tip: opposite numbers cancel, so pairs like \(a\) and \(-a\) give zero when summed.
Frequently asked questions
What is the correct answer to this question?
\(0\)
Why is this the correct answer?
The x-intercepts are the polynomial's zeroes, here \(a,\;0,\;-a\). Their sum is \(a+0+(-a)=0\). The distractor \(2a\) might come from adding absolute values incorrectly; \(-a\) is only one root, not the sum. Exam tip: opposite numbers cancel, so pairs like \(a\) and \(-a\) give zero when summed.
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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