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      Question

      In each of these questions, two equations (I) and (II)

      are given.You have to solve both the equations and give answer    I. x² - 8x + 15 = 0                                  II. y² - 3y + 2 = 0
      A X > Y Correct Answer Incorrect Answer
      B X < Y Correct Answer Incorrect Answer
      C X ≥Y Correct Answer Incorrect Answer
      D X ≤ Y Correct Answer Incorrect Answer
      E Relation cannot be established Correct Answer Incorrect Answer

      Solution

      x2 −8x +15 = 0 ⇒ x2 −5x − 3x +15 = 0  ⇒ x(x − 5) − 3(x −5) = 0  ⇒ (x −3)(x − 5) = 0  ∴ x = 3 or 5  II. y2 − 3y + 2 = 0 ⇒ y2 − 2y − y + 2 = 0  ⇒ y(y − 2) − 1(y − 2) = 0  ⇒ (y − 1)(y − 2) = 0  therefore, y = 1 or 2  Hence, x > y   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 = x = 3, 5 So, roots of second equation = y = 1, 2 After comparing roots of quadratic equation we can conclude that x > y.

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