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AP EAMCET202420 May 2024Evening ShiftMathematicsQuadratic EquationActual

Let [r] denote the largest integer not exceeding r and the roots of the equation 3 x^2+6 x+5+ (x^2+2 x+2 )=0 are complex numbers whenever L and M . If ( L - M ) is minimum, then greatest value of [r] such that L y^2+ M y+r 0 for all y R is,

Options

  1. AL
  2. BM
  3. CL + M
  4. DM - L

Correct answer

A. L

Step-by-step solution

3 x^2+6 x+5+ (x^2+2 x+2 )=0 aligned & ( +3) x^2+(2 +6) x+2 +5=0 & Roots are complex D 0 & (2 +6)^2-4( +3)(2 +5) 0 & - ^2-5 -6 0 & ^2+5 +6 0 ( +3)( +2) 0 & -3 ; -2 & ~L =-2, M =-3, ~L - M =1 & ~L y^2+ M y+r 0 & -2 y^2-3 y+r 0 y R & D 0 & 9+8 r 0 r - 9 8 aligned Maximum value of [r]=-2= L

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