Construct a companion matrix

CJam, 32 31 28 bytes

0q~)f/f-_,(_,\0a*1+fm<~]W%z

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This takes the input in ascending order, using the CJam list format. Sample input:

[-4.0 -7.0 13.0]

Explanation:

0     Push a 0 for later sign inversion.
q~    Get and interpret input.
)     Pop off last value.
f/    Divide all other values by it.
f-    Invert sign of values.
_,    Get count of values, which corresponds to n.
(     Decrement by 1.
_,    Create list of offsets [0 1 ... n-1] for later.
\     Swap n-1 back to top.
0a*   Create list of n-1 zeros.
1+    Append a 1. This is the second-but-last column [0 0 ... 0 1].
fm<   Apply rotation with all offsets [0 1 ... n-1] to column.
~     Unwrap the list of 0/1 columns.
]     Wrap all columns
W%    Invert their order from last-to-first to first-to last.
z     Transpose to get final matrix.
`     Convert to string for output.

APL, 40 30 bytes

{(-n↑⍵÷⊃⊖⍵),⍨⍉1↓⍉∘.=⍨⍳n←1-⍨≢⍵}

Accepts input in ascending order.

Explanation:

{
                        n←1-⍨≢⍵    ⍝ Define n = length(input)-1
                   ∘.=⍨⍳           ⍝ Create an n×n identity matrix
               ⍉1↓⍉                ⍝ Drop the leftmost column
            ,⍨                     ⍝ Append on the right:
  (-n↑⍵                            ⍝ n negated coefficients,
       ÷⊃⊖⍵)                       ⍝ divided by the n+1st
}

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CJam, 23 20 bytes

{)W*f/_,,_ff=1f>\.+}

This is a function that pops the input (ascending order) from the stack and pushes the output in return.

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How it works

)   e# Pop the last element from the input array.
W*  e# Multiply it by -1.
f/  e# Divide the remaining array elements by this product.
_,  e# Push a copy of the array and compute its length (L).
,_  e# Push [0 ... L-1] twice.
ff= e# For each I in [0 ... L-1]:
    e#   For each J in [0 ... L-1]:
    e#     Push (I==J).
    e# This pushes the L x L identity matrix.
1f> e# Discard the first element of each row, i.e., the first column.
\   e# Swap the result with the modified input.
.+  e# Vectorized append; append the input as a new column.