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From \( f(1) = 0 \): - Simpleprint

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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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:
\( f(0) = 4 \) ✓
\( f(1) = -1 -2 + 4 = 1 \) ✓
\( f(2) = -4 -4 + 4 = -4 \) ✓
The polynomial is \( \boxed{-x^2 - 2x + 4} \).

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