The complex number $$\(1+2 \mathrm{i}\)$$ is denoted by $$\(u\)$$. The polynomial $$\(2 x^{3}+a x^{2}+4 x+b\)$$, where $$\(a\)$$ and $$\(b\)$$ are real constants, is denoted by $$\(\mathrm{p}(x)\)$$. It is given that $$\(u\)$$ is a root of the equation $$\(\mathrm{p}(x)=0\)$$. Find the values of $$\(a\)$$ and $$\(b\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Answer:

Knowledge points:

Solution: