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Real Valued Functions

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Question

Find the values of p and q so that by $x^{4} + x^{3} + 8 x^{2} + p x + q$ is divisible by $x^{2} + 1$ . [Hint: Perform long division and then put remainder = 0]

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Solution

$\Rightarrow p - 1 = 0, q - 7 = 0$
$∴ p = 1, q = 7$

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