How many integers x satisfy the equation
(x^2 - 4x + 5)x^2 + x = 1
3
0
more than 4
4
2

• for any values of x, the terms (x^2-4x+5) & x^2 is always positive
  also x is an integer so x^2>=x
  hence there is no integral soln of given equation.
  ANS-0
  
  
• 11 years agoHelpfull: Yes(24) No(4)
• ans=4
  as x4
• 11 years agoHelpfull: Yes(9) No(6)
• after simplification it is a 4th degree eqn so it has 4 roots
  but we have to find integeral value of x,there is no integral root of eqn bcoz in eqn
  (x^2 - 4x + 5)x^2 + x = 1
  
  value of (x^2 - 4x + 5) is always +ve for any value of x
  so (x^2 - 4x + 5)x^2 >0 for any x(x^2>0)
  for any integer (x^2 - 4x + 5)x^2 + x never equals to 1
  check for -2,-1,0,1,2 etc
  hence there is no integer value of x.
  
• 11 years agoHelpfull: Yes(7) No(0)
• (x2-4x+5)x2+x=1
  x4-4x3+5x2+x-1=0
  here we get a fourth order equation.therefore it has 4 roots
• 11 years agoHelpfull: Yes(3) No(2)
• if x=1, LHS=3 if x=2 LHS=6 (increasing LHS for increasing x)
  if x=-1 LHS=9 if x=-2 LHS=66 (increasing LHS for decreasing x)
  and if x=0, LHS=0.
  sol. is 0
  
• 11 years agoHelpfull: Yes(3) No(1)
• i dont get the Question and answer both guys....
• 11 years agoHelpfull: Yes(2) No(2)
• ans= 0
  since ( x^2 - 4x+ 5) has imaginary roots. so no integer will satisfy the above mentioned equation
• 11 years agoHelpfull: Yes(2) No(1)
• ans is 0 as no integer value is satisfying above eqn
• 11 years agoHelpfull: Yes(2) No(0)
• rakesh kumar pls explain it in details.....
• 11 years agoHelpfull: Yes(2) No(1)
• 4 as after multiplying we get a fourth order eqn which must hav 4 roots
• 11 years agoHelpfull: Yes(1) No(4)
• ans:4
  becoz the highest power of x is 4 in given equation
• 11 years agoHelpfull: Yes(0) No(1)
• f(x)= x4-4x3+5x2+x-1=0
  change in sign 3 so 3 +ve real roots
  again f(-x)=x4+4x3+5x2-x-1=0
  change in sign =1 so 1 -ve real root so total 4 integer will satisfy the eqn
  hence 4 is the ans.....
  (if roots are not real they are imaginary not integers so check this out)
• 11 years agoHelpfull: Yes(0) No(1)