how many values of c in equation x^2-5x+c result rational roots which are integers.

(a) 1 (b) 3 (c) 6 (d) infinite

• w.k.t D=b^2- 4 a c >0 for rational roots
  = (-5)^2-4*1*c > 0
  hence values of c can be either positive or negative
  c=0,1,,2,3,4,5,-1,-2,-3,-4,-5...
  there is no unique values for c hence ans. will be infinte..option d is correct
• 8 years agoHelpfull: Yes(10) No(2)
• its mentioned that the roots have to integers, which implies both positive as well as negative integers. Also there is no such constraint on c if it has to be positive or negative.
  Such a condition can be satisfies by infinite values of c.
  For eg. X^2-5X-36, which have roots 9, -4
  X^2-5X-14, which have roots 7, -2
• 8 years agoHelpfull: Yes(2) No(3)
• for rational roots...
  b^2-4ac>0
  =>25-4*1*c>0
  =>25>4c
  =>cc can be6 ,5, 4,3,2,1,0........
  (since they all are integers)
  so, ans is infinite.
• 8 years agoHelpfull: Yes(2) No(2)
• the value of c can either be 4, 6 or 0 so ans is 3
• 8 years agoHelpfull: Yes(0) No(7)
• ans:6 sol: -3*-2=6
• 8 years agoHelpfull: Yes(0) No(2)
• Ans: d)infinite
  See this link for explanation: https://www.quora.com/How-many-values-of-C-in-the-equation-x-2-5x+c-result-in-rational-roots-which-are-integers
• 8 years agoHelpfull: Yes(0) No(2)