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Home » f(3) = (3)^2 - 6(3) + k = 0 - AMAZONAWS

f(3) = (3)^2 - 6(3) + k = 0 - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 At $x = \omega$:

📌 $(-\omega) + 3(-1) + (-2)(\omega - 1) + \omega + 5 = -\omega - 3 -2\omega + 2 + \omega + 5$

📌 Combine: $(-\omega -2\omega + \omega) = -2\omega$, $(-3 + 2 + 5) = 4$ â $-2\omega + 4$

📌 So $a = -2$, $b = 4$

📌 But let's verify with another point or use polynomial identity.

📌 Let $D(x) = x^4 + 3x^3 - 2x^2 + x + 5$, $D(x) = (x^2 - x + 1)(x^2 + ax + b) + (-2x + 4)$

📌 Compute RHS:

📌 $(x^2 - x + 1)(x^2 + ax + b) = x^4 + ax^3 + bx^2 - x^3 - ax^2 - bx + x^2 + ax + b = x^4 + (a-1)x^3 + (b-a+1)x^2 + (a-b)x + b$

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