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      Question

      I. 2p2 + 5p + 2 = 0               II.

      2q2 + 11 q + 14 = 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 + 5p + 2 = 0   (2p + 1) (p + 2) = 0   p = - (1/2)  or -2   II. 2q2 + 11 q + 14 = 0   (q + 2) (2q + 7) = 0   q = -2 or - (7 /2)   Hence, p ≥ q   Alternate Method:   if signs of quadratic equation is +ve and +ve respectively then the roots of equation will be -ve and -ve. 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 = -2, -7/2 After comparing roots of quadratic eqution we can conclude that p ≥ q.

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