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      Question

      I. p2 +7p + 10 = 0 II. q2 - q

      – 6 = 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. p2 +7p + 10 = 0,
      p2+ 5p + 2p + 10 + 6 = 0; or
      p( p+5) + 2( p+5) = 0
      (p+2)( p+5) = 0, or p = -2 or = -5,
      II. q2 - q – 6 = 0;
      q2 – 3q + 2q – 6 = 0
      q(q-3) + 2(q -3) = 0 or, q = -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.
      So, roots of first equation = p = -2, -5
      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 second equation = q = -2, 3
      After comparing roots of quadratic eqution we can conclude that q ≥ p.

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