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AP EAMCET202420 May 2024Morning ShiftMathematicsQuadratic EquationActual

If and are two double roots of x^2+3(a+3) x-9 a=0 for different values of ( ) . then the minimum value of x^2+ x- =0 is

Options

  1. A69 4
  2. B- 69 4
  3. C- 35 4
  4. D35 4

Correct answer

B. - 69 4

Step-by-step solution

For double roots D=b^2-4 a c=0 9(a+3)^2+36 a=0 a^2+10 a+9=0 (a+9)(a+1)=0 a=-1,-9 For a=-1 , equation becomes x^2+6 x+9=0 x=-3 For a=-9 equation becomes x^2-18 x+81=0 x=9 =9, =-3( ) Now, given equation becomes x^2+9 x+3=0 (x+ 9 2 )^2- 69 4 =0 We know that (x+ 9 2 )^2 0 (x+ 9 2 )^2- 69 4 - 69 4 Hence, minimum value = -69 4

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