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    Question

    I. 2p2 - 3p – 2 = 0 II. 2q2

    - 11q + 15 = 0 In each question two equations are provided. On the basis of these you have to find out the relation between p and q. Give answer.
    A if p = q Correct Answer Incorrect Answer
    B if p > q Correct Answer Incorrect Answer
    C if q > p Correct Answer Incorrect Answer
    D if p ≥ q Correct Answer Incorrect Answer
    E if q ≥ p Correct Answer Incorrect Answer

    Solution

    I. 2p2 - 3p – 2 = 0,
    (2p + 1)( p - 2) = 0
    p = - (1/2) or 2,
    II. 2q2 - 11q + 15 = 0
    (2q - 5) (q - 3) = 0,
    q = (5/2) or 3;
    Hence, q > p.
    Alternate Method:
    if signs of quadratic equation is -ve and -ve respectively then the roots of equation will be -ve and +ve. (note: -ve sign will come in smaller root)
    So, roots of first equation = p = -1/2, 2
    if signs of quadratic equation is -ve and +ve respectively then the roots of equation will be +ve and +ve.
    So, roots of second equation = q = 5/2, 3
    After comparing roots of quadratic eqution we can conclude that q > p.

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