Question:medium
Let \( \alpha, \alpha + 2 \in \mathbb{Z} \) be the roots of the quadratic equation}
\[
x(x+2) + (x+1)(x+3) + (x+2)(x+4) + \cdots + (x+n-1)(x+n+1) = 4n
\]
for some \( n \in \mathbb{N} \). Then \( n + \alpha \) is equal to:
Let \( \alpha, \alpha + 2 \in \mathbb{Z} \) be the roots of the quadratic equation}
\[
x(x+2) + (x+1)(x+3) + (x+2)(x+4) + \cdots + (x+n-1)(x+n+1) = 4n
\]
for some \( n \in \mathbb{N} \). Then \( n + \alpha \) is equal to:
Updated On: Apr 10, 2026
- \(0\)
- \(1\)
- \(2\)
- \(3\)
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The Correct Option is C
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