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AP EAMCET202022 Sep 2020Evening ShiftMathematicsQuadratic EquationActual

For which value of ' k ', the roots of equation 2 x^2+5 x+k=0 are rational?

Options

  1. A5 8
  2. B25 8
  3. C25 4
  4. D5 4

Correct answer

B. 25 8

Step-by-step solution

Given, quadratic equation is 2 x^2+5 x+k=0 Quadratic equation have rational roots when D is perfect square, aligned & D=b^2-4 a c=25-4 2 k & D=25-8 k aligned from options checking k= 25 8 makes D is perfect square k= 25 8 Hence, option (2) is correct.

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