1. The problem statement, all variables and given/known data Consider the polynomial ##p(x) = x^4 + ax^3 + bx^2 + cx + d##, where a, b, c, d ∈ ℝ. Given that 1 + i and 1 - 2i are zeroes of p(x), find the values of a, b, c and d. 2. Relevant equations 3. The attempt at a solution Since 1 + i and 1 - 2i are zeroes, I believe it follows that 1 - i and 1 + 2i should also be zeroes, right? Hence, plugging in 1 + i, 1 - i, 1 + 2i, 1 - 2i should produce equations that equal 0, assuming I'm remembering the factor theorem correctly. But, I'm not sure where to go from there. Solving this through brute force would be ridiculous and inefficient, but I can't think of how else I can solve this. Anyhow, I plugged in the factors and got the following equations, I just don't know what to do with them: ##p(1 + i) = (-4 - 2a + c + d) + (2a + 2b + 2c)i = 0## ##p(1 - i) = (-4 - 2a + c + d) - (2a + 2b + 2c)i = 0## ##p(1 + 2i) = (-7 - 11a - 3b + c + d) + (-24 - 2a + 4b + 2c)i = 0## ##p(1 - 2i) = (-7 - 11a - 3b + c + d) - (-24 - 2a + 4b + 2c)i = 0## How can I solve for these variables efficiently?