What is the sum of the irrational roots of the equation (x-1)(x-3)(x-5)(x-7)=9 ?



a) 10
b) 8
c) 6
d) 4

• Given that
  (x - 1) (x - 3) (x - 5) (x - 7) = 9
  
  Let x - 4 = p
  Then the given eqn becomes
  (p + 3) (p + 1) (p - 1) (p - 3) = 9
  (p2 - 1) (p2 - 9) = 9
  p4 - 10p2 + 9 = 9
  p2 (p2 - 10) = 0
  p2 =0 or p2-10 =0
  p = 0 or p = sqrt(10) or p = - sqrt(10)
  then x - 4 = 0, x - 4 = sqrt(10) or x - 4 = - sqrt(10)
  Now the roots of the given eqn are 4,4 + sqrt(10) and 4 - sqrt(10)
  The irrational roots are 4+sqrt(10) and 4 - sqrt(10)
  The sum of the irrational roots = 4 + sqrt(10) + 4 - sqrt(10) = 8.
  
  Hence the answer is 8.
• 7 years agoHelpfull: Yes(23) No(3)
• (4-1)(4-3)(4-5)4-7)=9
  
• 7 years agoHelpfull: Yes(9) No(7)
• how did you get 4 in the solution
• 7 years agoHelpfull: Yes(9) No(0)