(i)[4]
With working shown, check that $u$ is a root of $p(x) = 0$, and then state one more complex root of the equation.
(ii)[6]
Determine the remaining two roots of $p(x) = 0$.
Mathematics 9709 · AS & A Level · Complex numbers
Complex numbers — practice question
Use $u$ to denote the complex number $1 + (\sqrt{2})i$. Write $x^4 + x^2 + 2x + 6$ as $p(x)$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substitute $x=1+\sqrt2 i$ and try expanding $x^2$ and $x^4$” …
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