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    Question

    If p3 + 9p2 + 8p + 13 =

    6p2 + 5p + 12, then find the value of {(p4 + 1/p2)}/(p2 + 3p + 1).
    A 1 Correct Answer Incorrect Answer
    B -2 Correct Answer Incorrect Answer
    D -4 Correct Answer Incorrect Answer

    Solution

    ATQ, Given, p3┬а+ 9p2┬а+ 8p + 13 = 6p2┬а+ 5p + 12 Or, p3┬а+ 9p2┬атАУ 6p2┬а+ 8p тАУ 5p + 13 тАУ 12 = 0 Or, p3┬а+ 3p2┬а+ 3p + 1 = 0 Since, (x + y)3 = x3┬а+ 3x2y┬а+ 3xy2┬а+ 1 Therefore, (p + 1)3 = 0 Or, p = -1 Therefore, {(p4┬а+ 1/p2 )}/(p2┬а+ 3p + 1) Putting p = -1, we get {(p4┬а+ 1/p2 )}/(p2┬а+ 3p + 1) = (1 + 1)/(1 тАУ 3 + 1) = -2

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