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AP EAMCET202119 Aug 2021Evening ShiftMathematicsQuadratic EquationActual

If a is a positive integer such that the roots of the equation 7 x 2 - 13 x + a = 0 are rational numbers, then the smallest possible value of a is

Options

  1. A5
  2. B6
  3. C7
  4. D8

Correct answer

B. 6

Step-by-step solution

Given, 7 x 2 - 13 x + a = 0 For rational roots D ≥ 0 and D must be perfect square. ⇒ 169 - 28 a ≥ 0 Now, we see from options that a = 7   &   a = 8 are not possible as then D < 0 . For a = 5 , D = 168 - 28 × 5 = 29 ≥ 0 But it is not perfect square. For a = 6 , D = 169 - 28 × 6 = 1 ≥ 0 and it is a perfect square. Hence, the smallest possible value of a is 6 .

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