If the x-axis intersections of a graph are \\((r-1,0),\ (r+2,0),\ (r+5,0)\\), what is the mean of the zeroes?
Answer and explanation
Correct answer: \(r+2\)
The zeroes (x-values where the graph meets the x-axis) are \(r-1,\ r+2,\ r+5\). Mean = \(\dfrac{(r-1)+(r+2)+(r+5)}{3}=\dfrac{3r+6}{3}=r+2\). The closest distractor \(r+1\) arises from arithmetic mistake; the correct procedure is sum all roots then divide by their count. Exam tip: always add the symbolic roots first, then divide by the number of roots to avoid sign or division errors.
Frequently asked questions
What is the correct answer to this question?
\(r+2\)
Why is this the correct answer?
The zeroes (x-values where the graph meets the x-axis) are \(r-1,\ r+2,\ r+5\). Mean = \(\dfrac{(r-1)+(r+2)+(r+5)}{3}=\dfrac{3r+6}{3}=r+2\). The closest distractor \(r+1\) arises from arithmetic mistake; the correct procedure is sum all roots then divide by their count. Exam tip: always add the symbolic roots first, then divide by the number of roots to avoid sign or division errors.
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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