how many values of c in the equation x^2-5x+c=0 results in rational roots which are integers?

• The value of x can be calculated as:
  x=( 5 +- sqrt(5^2 -4c))/2
  For c = 0 , 4 , 6 , -6, -14, -24 , -36, -50 ……….and so on we can get rational roots which are
  Integers.
  Hence the Answer is :- Infinite
• 8 years agoHelpfull: Yes(10) No(2)
• Since leading coefficient is one and coefficient of x is integer i.e -5 so for every integral value of 'c' for which equation has rational roots. then these rational roots must be integral.
  and c is of the form given by
  
  25 - 4c = (2*n +_ 1)^2
  
  c =( 25 - (2*n +_ 1)^2)/4
  
  n belongs to integer
  
  so there exists "Infinitely" many c !!
• 8 years agoHelpfull: Yes(2) No(1)
• will u plz explain????? santosh uplawdiya
• 8 years agoHelpfull: Yes(0) No(1)
• Please explain in detail
• 8 years agoHelpfull: Yes(0) No(0)