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Home » \(n^2 + n - 10100 = 0\). - Dachbleche24

\(n^2 + n - 10100 = 0\). - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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Solution: Let \( f(x) = ax^2 + bx + c \). Use the given conditions:
\( f(0) = c = 4 \)
\( f(1) = a + b + c = 1 \) → \( a + b + 4 = 1 \) → \( a + b = -3 \)
\( f(2) = 4a + 2b + c = -4 \) → \( 4a + 2b + 4 = -4 \) → \( 4a + 2b =...
a + b = -3 \\
2a + b = -4
Subtract the first from the second: \( (2a + b) - (a + b) = -4 - (-3)...
Substitute into \( a + b = -3 \): \( -1 + b = -3 \) → \( b = -2 \)
So \( f(x) = -x^2 - 2x + 4 \).
Verify:

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