- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,878

- Thread starter anemone
- Start date

- Thread starter
- Admin
- #1

- Feb 14, 2012

- 3,878

- Moderator
- #2

- Feb 7, 2012

- 2,765

$c$ and $d$ satisfy the equation $(x^2-4)^2 = 5+x$, or $x^4 - 8x^2 - x + 11 = 0\quad(**).$

But if $x$ satisfies (**) then $-x$ satisfies (*). So the roots of (*) are $a,b,-c,-d.$ Thus $abcd$ is the product of the roots of (*), namely 11.

- Thread starter
- Admin
- #3

- Feb 14, 2012

- 3,878

Well done,

$c$ and $d$ satisfy the equation $(x^2-4)^2 = 5+x$, or $x^4 - 8x^2 - x + 11 = 0\quad(**).$

But if $x$ satisfies (**) then $-x$ satisfies (*). So the roots of (*) are $a,b,-c,-d.$ Thus $abcd$ is the product of the roots of (*), namely 11.