Prove-that-if-a-bi-is-a-root-to-pz-2-qz-r-0-where-a-b-p-q-r-R-then-a-bi-is-also-a-root-to-that-equation-

Tinku Tara June 4, 2023 Others 0 Comments

Question Number 98924 by Rio Michael last updated on 17/Jun/20

Prove that if a+ bi is a root to pz^2 + qz + r = 0 , where a,b,p,q,r ∈R then a−bi is also a root to that equation.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{if}\:{a}+\:{bi}\:\mathrm{is}\:\mathrm{a}\:\mathrm{root}\:\mathrm{to} \\ $$$$\:{pz}^{\mathrm{2}} \:+\:{qz}\:+\:{r}\:=\:\mathrm{0}\:,\:\mathrm{where}\:{a},{b},{p},{q},{r}\:\in\mathbb{R} \\ $$$$\mathrm{then}\:{a}−{bi}\:\mathrm{is}\:\mathrm{also}\:\mathrm{a}\:\mathrm{root}\:\mathrm{to}\:\mathrm{that}\:\mathrm{equation}. \\ $$

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Prove-that-if-a-bi-is-a-root-to-pz-2-qz-r-0-where-a-b-p-q-r-R-then-a-bi-is-also-a-root-to-that-equation-

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