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Question
Find the value of 2x4 + 5x3 + 7x2 – x + 41, when x = `-2 - sqrt(3)"i"`.
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Solution
x + 2 = `- sqrt(3)"i"` ⇒ x2 + 4x + 7 = 0
Therefore, 2x4 + 5x3 + 7x2 – x + 41
= (x2 + 4x + 7)(2x2 – 3x + 5) + 6
= 0 × (2x2 – 3x + 5) + 6
= 6
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