2) How many values of C in the equation x^2 – 5C + C result in rational roots which are
integers?

• something is missing in this question.the question should be x^2 - 5cx + c
  the linear coefficient is the opposite of the sum of the roots and the constant term is their product. That is,
  
  (x−r1) (x−r2) =x2 − (r1+r2)x + r1r2(x−r1)(x−r2) = x2 − (r1+r2)x + r1r2
  so here r1=k and r2=5-k and c=r1r2
  roots are
  r1 r2 c
  0 5 0
  1 4 4
  2 3 6
  . . .
  . . .
  . . .
  .
• 8 years agoHelpfull: Yes(0) No(5)
• where has the 'c' gone from '5cx'? @akanksha
• 8 years agoHelpfull: Yes(0) No(2)
• Where is the answer? @AKANKSHA JAISWAL
• 8 years agoHelpfull: Yes(0) No(1)
• x^2-5c+c=0
  => x=sqrt(5c-c)
  now put the values of c by hit and trial method
  so x=2 for c=1 and x=4 for c=4
  the values of x are rational no intergers.
• 8 years agoHelpfull: Yes(0) No(4)
• ans is ---4
  
  we have,by quadratic roots x= -b+-(b^2-4ac)/2a
  so, if we check the possible values of c which outcomes the value of x as rational integers.
  we will have
  
  
  0,4,6,-6 are the possible values of c
• 8 years agoHelpfull: Yes(0) No(2)
• value of C will be infinite.
• 1 year agoHelpfull: Yes(0) No(0)