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if t^2-12x t-(f(x)+64x)=0 has one root twice the other .x belongs to R. find maximum value of f(x)

if t^2-12x t-(f(x)+64x)=0 has one root twice the other .x belongs to R. find maximum value of f(x)

Grade:12th pass

1 Answers

Vikas TU
14149 Points
6 years ago
Dear Student,
given quadratic equation: t^2-12xt-(f(x)+64x)=0
roots are: (12x±sqrt(144x^2+4f(x)+64*4x))/2
  1. ±2*sqrt(36x^2+f(x)+64x)/2=6x±sqrt(36x^2+f(x)+64x)
as one root is twice the other,
  1.  
  2.  
  3.  
or f(x)=-32x^2-64x
here f(x) is a quad eqn with D>=0 and a
so maximum value at x=-b/2a =64/(2* -32) = -1
therefore, maximum value of f(x)= f(-1)=-32(-1)^2-64(-1)
=32 (Ans.)
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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