Multiple Choice Questions on If the equations x2 px q 0 and x2 qx p 0 have a common root then which one of the following is ........... for CDS Exam Preparation

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Multiple Choice Questions

If the equations x2 px q 0 and x2 qx p 0 have a common root then which one of the following is ...........

Quantitative Aptitude (CDS) Quadratic Equations
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    If the equations x2- px + q=0 and x2 + qx - p = 0 have a common root, then which one of the following is  correct?

    p − q = 0

    Incorrect Answer

    p + q − 2 = 0

    Incorrect Answer

    p + q − 1 = 0

    Incorrect Answer

    p − q − 1 = 0

    Correct Answer
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    Explanation:

    Here a= 1, b = − p, c = q and a' = 1, b' = q, c' = − p
    Applying common root condition,
    (a'c − ac')2 = (bc' − b'c)(ab' − a'b)
    => (q + p)2 = (p2 − q2 ) (q + p)
    => (p + q) = (p − q) (p + q)
    => p − q = 1
    => p − q − 1 = 0

    By: Munesh Kumari
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