Let-p-x-ax-2-bx-c-be-such-that-p-x-takes-real-values-for-real-values-of-x-and-non-real-values-for-non-real-values-of-x-Prove-that-a-0-and-find-all-possible-values-of-c-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 62844 by alphaprime last updated on 25/Jun/19

Let p(x) = ax^2 + bx + c be such that p(x) takes real values for real values of x and non−real values for non−real values of x . Prove that a = 0 and find all possible values of c.

$${Let}\:{p}\left({x}\right)\:=\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:\:{be}\:{such}\:{that}\:{p}\left({x}\right)\:{takes}\:{real}\:{values} \\ $$$${for}\:{real}\:{values}\:{of}\:{x}\:{and}\:{non}−{real}\:{values}\:{for}\:{non}−{real} \\ $$$${values}\:{of}\:{x}\:.\:{Prove}\:{that}\:{a}\:=\:\mathrm{0}\:{and}\:{find}\:{all} \\ $$$${possible}\:{values}\:{of}\:{c}. \\ $$

Answered by ajfour last updated on 29/Sep/23

$${c}=\mathrm{3}\:? \\ $$

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Let-p-x-ax-2-bx-c-be-such-that-p-x-takes-real-values-for-real-values-of-x-and-non-real-values-for-non-real-values-of-x-Prove-that-a-0-and-find-all-possible-values-of-c-

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