Find the other roots of this equation. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_33 Year：2021 Question No：10(b)

Answer:

State second root \(-1-\sqrt{2} \mathrm{i}\)
Carry out a method to find a quadratic factor with zeros \(-1 \pm \sqrt{2} \mathrm{i}\)
Obtain \(z^{2}+2 z+3\)
Commence division and reach partial quotient \(z^{2}+k z\)
Obtain second quadratic factor \(z^{2}-2 z+4\)
Solve a 3-term quadratic and use \(i^{2}=-1\)
Obtain roots \(1+\sqrt{3} i\) and \(1-\sqrt{3} i\)

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.)

Answer:

Knowledge points:

Solution:

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