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AP EAMCET202124 Aug 2021Evening ShiftMathematicsQuadratic EquationActual

Which of the following condition imply that roots of the equation ( 1 4 ) x^2+b x+c=0 are integers?

Options

  1. Ab^2-c>0
  2. Bb and c are even integers
  3. Cb^2-c is the square of an integer and b is an integer
  4. Db and c are integers

Correct answer

C. b^2-c is the square of an integer and b is an integer

Step-by-step solution

We have, 1 4 x^2+b x+c=0 By using quadratic formula x= -b b^2-4 1 4 c 2 1 4 x= -b b^2-c 1 2 The roots are integer iff b is an integer and b^2-c is perfect square.

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