Freeflows
Polynomial Roots Product 2
Let $ r_1, $ $ r_2, $ $ \dots, $ $ r_7 $ be the distinct complex roots of the polynomial $ P(x) = x^7 - 7 $. Let \[K = \prod_{1 \le i < j \le 7} (r_i + r_j).\]In other words, $ K $ is the product of all numbers of the of the form $ r_i + r_j, $ where $ i $ and $ j $ are integers for which $ 1 \le i < j \le 7 $. Determine $ K^2 $.
- 1
- 2
- 3
- +
- 4
- 5
- 6
- -
- 7
- 8
- 9
- $\frac{a}{b}$
- .
- 0
- =
- %
- $a^n$
- $a^{\circ}$
- $a_n$
- $\sqrt{}$
- $\sqrt[n]{}$
- $\pi$
- $\ln{}$
- $\log$
- $\theta$
- $\sin{}$
- $\cos{}$
- $\tan{}$
- $($
- $)$
- $[$
- $]$
- $\cap$
- $\cup$
- $,$
- $\infty$