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

Mathematics
IGCSE&ALevel
CAIE
Exam No:9709_w21_qp_31 Year:2021 Question No:10(b)

Answer:

State second root \(1-2 i\)

Knowledge points:

3.9.3 use the result that, for a polynomial equation with real coefficients, any non-real roots occur in conjugate pairs (e.g. in solving a cubic or quartic equation where one complex root is given.)

Solution:

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