What is the product of the irrational roots of the equation (2x-1)(2x-3)(2x-5)(2x-7)=9?

• (2x - 1) (2x - 3) (2x - 5) (2x - 7) = 9
  let 2x - 4 = p
  
  or (p + 3) (p + 1) (p - 1) (p - 3) = 9
  or (p^2 - 1) (p^2 - 9) = 9
  or p^4 - 10p^2 + 9 = 9
  or p^2 (p^2 - 10) = 0
  or p = 0 or ± root 10
  2x-4= ± root 10
  x= (1/2) [4± root 10]
  product of roots = (1/2) [4+ root 10]*(1/2) [4- root 10] = (1/4)*(16-10) =3/2
• 12 years agoHelpfull: Yes(27) No(9)
• Product is 3/2
  Expln :
  (2x - 1) (2x - 3) (2x - 5) (2x - 7) = 9
  Let 2x - 4 = y
  
  => (y + 3) (y + 1) (y - 1) (y - 3) = 9
  => (y^2 - 1) (y^2 - 9) = 9
  => y^4 - 10y^2 + 9 = 9
  => y^2 (y^2 - 10) = 0
  => y = 0 or ± 8730;(10)
  => 2x - 4 = ± 8730;(10)
  => x = (1/2) [4 ± 8730;(10)]
  => product of the irrational roots
  = (1/2)^2 * [4 + 8730;(10)] [4 - 8730;(10)]
  = (1/4) * 6
  = 3/2.
• 12 years agoHelpfull: Yes(10) No(7)
• (2x-1)(2x-3)(2x-5)(2x-7)=9
  let 2x-4=y
  (y+3)(y-3)(y)
  (y^2 - 1) (y^2 - 9) = 9
  => y^4 - 10y^2 + 9 = 9
  => y^2 (y^2 - 10) = 0
  => y = 0 or ± √(10)
  => 2x - 4 = ± √(10)
  => x = (1/2) [4 ± √(10)]
  => product of the irrational roots
  = (1/2)^2 * [4 + √(10)] [4 - √(10)]
  = (1/4) * 6
  = 3/2.
• 12 years agoHelpfull: Yes(6) No(4)