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      Question

      I. p2 + 2p – 8 = 0 II. q2

      – 5q + 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 + 2p – 8 = 0
      ⇒ (p + 4) ( p – 2) = 0
      ⇒ p = 2, - 4
      II. q2 – 5q + 6 = 0
      ⇒ ( q - 3) ( q - 2) = 0
      ⇒ q = 2, 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 larger root)
      So, roots of first equation = p = 2, -4
      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, 3
      After comparing roots of quadratic eqution we can conclude that q ≥ p.

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