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AP EAMCET202418 May 2024Morning ShiftMathematicsQuadratic EquationActual

For real values of x and a , if the expression x+a 2 x^2-3 x+1 assumes all real values, then

Options

  1. Aa -1 or a - 1 2
  2. B-1 a - 1 2
  3. C1 2 a 1
  4. Da 1 2 or a 1

Correct answer

B. -1 a - 1 2

Step-by-step solution

aligned & Let x+a 2 x^2-3 x+1 =y, where y R & x+a=2 y x^2-3 y x+y aligned aligned & 2 y x^2-(3 y+1) x+y-a=0 & (3 y+1)^2-4.2 y(y-a) 0 aligned ( x R ) aligned & 9 y^2+1+6 y-8 y^2+8 a y 0 & y^2+(8 a+ b) y+1 0 aligned aligned & 1 0 and (8 a+b)^2-4.1 .1 0 & 64 a^2+36+96 a-4 0 & (2 a+1)(a+1) 0 aligned -1 a - 1 2

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