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Home » To find $\vecw$, we compute the linear combination: - Abbey Badges

To find $\vecw$, we compute the linear combination: - Abbey Badges

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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So \(a\omega + b = 3\omega + 4\), hence \(a = 3\), \(b = 4\).
Similarly, check at \(\omega^2\) (the conjugate root), but since coeff...
Verify using algebra:
x^4 + 3x^3 - 2x^2 + x + 5 = (x^2 - x + 1)(x^2 + ax + b) + ax + c
Expand right-hand side:
= x^4 + (a - 1)x^3 + (b - a + 1)x^2 + (-b + a)x + b
Add \(ax + c\):
x^4 + (a - 1)x^3 + (b - a + 1)x^2 + (-b + a + a)x + (b + c) = x^4 + (a...
Match coefficients:
\(x^4\): 1 = 1 â

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