Find the general form of all real polynomials of least degree which have zeros 2 + i and -1 + 3i

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02-12-2017
Mathematics

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Find the general form of all real polynomials of least degree which have zeros 2 + i and -1 + 3i

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Rod44 Rod44 · Answer 1 · 2017-12-02T16:45:52+01:00

Rod44 Rod44

02-12-2017

The coefficients must be real so each complex root must have a conjugate: 2-i and -1-3i.
The factorisation is (x-2-i)(x-2+i)(x+1-3i)(x+1+3i)=(x²-4x+5)(x²+2x+10).
Expanded this is:
x⁴+2x³+10x²
-4x³-8x²-40x
+5x²+10x+50=

x⁴-2x³+7x²-30x+50.

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