If anyone knows this me. answer only if you know. more points for you if answered!

1a) Possible rational roots will be of the form
  ±{divisor of 10}/{divisor of 4}
Divisors of 10 are {1, 2, 5, 10}
Divisors of 4 are {1, 2, 4}

Then possible rational roots are
  {±1/4, ±1/2, ±1, ±5/4, ±2, ±5/2, ±5, ±10}

1b) Your answer is correct.

2) One additional root will be the conjuate of the given complex root.
  5 -3i

3) If one root is 5 -√7, another will be 5 +√7. Then your polynomial is
  P(x) = (x -(5 -√7))*(x -(5 +√7)) = (x -5)^2 -(√7)^2
  P(x) = x^2 -10x +18

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