# Problem 1:
polyroot( c(1, -1, -1, 1) )

# Problem 3:
polyroot( c(1, 1, 1, 1) )

# Problem 6:
polyroot( c(1, 0, 2, 0, 1) )

# Problem 7:
polyroot( c(1, 0, 0, 1) )

# Problem 10:
polyroot( c(1, 0, 1, 0, 1) )

# Problem 11:
A = matrix( c(1, 1, 1,
              0, 1, 2,
              0, 1, 4), nrow=3, ncol=3, byrow=TRUE )
b = c(1, 0, 0)
solve(A, b) 

# Problem 12:
polyroot( c(-12, 8, 1, 2, 1) )

A = matrix( c(1, 1, 1, 0,
              1, -3, 0, 2,
              1, 9, -4, 0,
              1, -27, 0, -8), nrow=4, ncol=4, byrow=TRUE )
b = c(3 + 0.35, 0 + 0.85, -1 - 0.45, 2 - 0.75)
solve(A, b) 

# Problem 15:
polyroot( c(1, 0, -2, 0, 1) )

# Problem 17:
polyroot( c(1, -1, -1, 1) )

# Problem 18:
polyroot( c(2, 2, 1) )