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AP EAMCET202423 May 2024Morning ShiftMathematicsQuadratic EquationActual

The set of all values of k for which the inequality x^2-(3 k +1)x+4 k ^2+3 k -3 0 is true for all real values of x is

Options

  1. A(- 13 7 , 1 )
  2. B(-1, 13 7 )
  3. C(- ,- 13 7 ) (1, )
  4. D(- ,-1) ( 13 7 , )

Correct answer

C. (- ,- 13 7 ) (1, )

Step-by-step solution

Since, x^2-(3 k+1) x+4 k^2+3 k-3 0 x R So, 1 0 and b^2-4 a c 0 aligned & -(3 k+1) ^2-4 1 (4 k^2+3 k-3 ) 0 & (7 k+13)(k-1) 0 aligned So, x (- , -13 7 ) (1, ) .

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