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      Question

      I. 195x² - 46x - 21 = 0 II. 209y² + 13y - 12 =

      0
      A x < y Correct Answer Incorrect Answer
      B x > y Correct Answer Incorrect Answer
      C x=y or no relationship cannot be established between x and y Correct Answer Incorrect Answer
      D x ≥ y Correct Answer Incorrect Answer
      E x ≤ y Correct Answer Incorrect Answer

      Solution

      I. 195x² - 46x - 21 = 0 195x² + 45x - 91x - 21 = 0 15x(13x + 3) - 7(13x + 3) = 0 (13x + 3) (15x – 7) = 0 ∴ x = 7/15, -3/13 II. 209y² + 13y - 12 = 0 209y² + 57y - 44y  - 12 = 0 19y(11y + 3) – 4(11y + 3) = 0 (19y – 4) (11y + 3) = 0 ∴ y = 4/19, -3/11 Hence, relationship cannot be established between x and y Alternate Method: Remember whenever constant value of both the quadratic equations are - ve, there is no need to find the exact value of roots. In this case, there will be always no relation between x & y. Hence relationship between x & y cannot be established.   

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