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AP EAMCET202420 May 2024Evening ShiftMathematicsQuadratic EquationActual

For any real value of x , if 11 x^2+12 x+6 x^2+4 x+2 (a, b] then the value x for which 11 x^2+12 x+6 x^2+4 x+2 =b-a+3 is

Options

  1. A3 4
  2. B3 2
  3. C2
  4. D- 1 2

Correct answer

D. - 1 2

Step-by-step solution

11 x^2+12 x+6 x^2+4 x+2 =y aligned & (11-y) x^2+(12-4 y) x+6-2 y=0 & For real value of x, D 0 & (12-4 y)^2-4(11-y)(6-2 y) 0 & y^2+2 y-15 0 & (y+5)(y-3) 0 & y -5 or y 3 & 11 x^2+12 x+6 x^2+4 x+2 (-5,3] b=3, a=-5 & 11 x^2+12 x+6 x^2+4 x+2 =11 & 12 x+6=44 x+22 -16=32 x & x= -1 2 aligned

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