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Complex Number Test - 3

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  • Question 1
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    If f (x) - g ( x6 ) + x4 h( x6 ) is divisible by x2 + x + 1, then

    Solution

    f (ω) = 0 ⇒ g (1) + ωh (1) = 0

    F (ω2 ) = 0 ⇒ g (1) + ω2 h (1) = 0

    ⇒ 2 g (1) + h (1) ( ω = ω2 ) = 0

    or, h (1) = 2g (1) ⇒ g (1) = 0 and h (1) = 0

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