if p(x)=ax^4+bx^3+cx^2+dx+e has roots at x=1,2,3,4 & p(0)=48.what is p(5)

• 
  48
  
  if 1 is a root then x-1 is a factor of p(x)
  similarly x-2 is a factor,x-3 ,x-4 are factors
  
  but p(x) is 4th degree polynomial therefore it can be in the form
  
  p(x) = Q(x-1)(x-2)(x-3)(x-4) , where Q is a constant
  
  but given p(0) =48
  
  therefore 24 Q =48
  
  Q=2
  
  p(x) =2(x-1)(x-2)(x-3)(x-4)
  
  p(5)= 2*4*3*2*1 = 48
• 12 years agoHelpfull: Yes(43) No(0)
• if 1 is the root then (x-1) is the factor of px,similarly
  (x-2),(x-3),(x-4) are factors.
  but p(x) is the 4th degree polynomial therefor it can be in the form
  p(x)=k(x-1)(x-2)(x-3)(x-4)
  
  where k is a constant
  but p(0)=48 given
  therefore 24k=48
  so k=2
  p(x)=2(x-1)(x-2)(x-3)(x-4)
  p(5)=2*4*3*2*1=48
• 12 years agoHelpfull: Yes(7) No(3)
• 24 is the ans
• 12 years agoHelpfull: Yes(2) No(20)