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Home » #### \(2\sqrt6\) - Groen Casting

#### \(2\sqrt6\) - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Therefore, the sum of the roots of the original equation is:

📌 Find the remainder when \( u^4 + 3 \) is divided by \( u^2 - 2u + 2 \).

📌 We are to divide \( u^4 + 3 \) by \( u^2 - 2u + 2 \) and find the remainder. Since the divisor is quadratic, the remainder must be linear or constant: let \( R(u) = au + b \).

📌 u^4 + 3 = (u^2 - 2u + 2)Q(u) + au + b

📌 To find \( a \) and \( b \), perform polynomial division or use substitution with roots of the divisor.

📌 Letâs use the roots of \( u^2 - 2u + 2 = 0 \). The discriminant is \( 4 - 8 = -4 \), so roots are:

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