11 HL: The Conjugate Root Theorem

Complete the question below before our next class.

Given that \(1+3i\) is a root of \(x^3 – 3x^2 + 12x-10=0\), find all other roots.

Hint

Note that \(1-3i\) will also be a root, and so \((x-(1+3i))(x-(1-3i))\) will divide the polynomial \(x^3 – 3x^2 + 12x-10\).