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Complex Number Test - 4

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Complex Number Test - 4
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    If f ( x ) and g ( x ) are two polynomials such that the polynomial h (x) = xf ( x3 ) + x2 g ( x6 ) is divisible by x2 + x + 1, then

    Solution

    The roots of x2 + x + 1 = 0 are w and w2

    So h (w) = 0 and h ( w2 ) = 0

    ⇒ wf (1) + w2 g (1) = 0 and w2 f (1) + wg (1) = 0

    ⇒ f (1) = g (1) = 0

    ∴ h (1) = f (1) + g (1) = 0

     

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