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AP EAMCET202422 May 2024Evening ShiftMathematicsQuadratic EquationActual

The set of all real values ' a ' for which -1 2 x^2+a x+2 x^2+x+1 3 holds for all real values of x is

Options

  1. A(-7,5)
  2. B(5, )
  3. C(1,5)
  4. D(- , 1)

Correct answer

C. (1,5)

Step-by-step solution

aligned & -1 2 x^2+a x+2 x^2+x+1 3 & Consider -1 2 x^2+a x+2 x^2+x+1 3 x^2+(a+1) x+3 0 & D 0 (a+1)^2-36 0 a^2+2 a-35 0 aligned (a+7)(a-5) 0 a (-7,5) ...(i) aligned & Also, 2 x^2+a x+2 x^2+x+1 3 -x^2+(a-3) x-1 0 & D 0 (a-3)^2-4 0 aligned a^2-6 a+5 0 (a-1)(a-5) 0 a (1,5) ...(ii) So, from (i) and (ii), a (1,5)

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