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

$L e t p (x) = {a x}^{2} + b x + c b e s u c h t h a t p (x) t a k e s r e a l v a l u e s$ $f o r r e a l v a l u e s o f x a n d n o n - r e a l v a l u e s f o r n o n - r e a l$ $v a l u e s o f x . P r o v e t h a t a = 0 a n d f i n d a l l$ $p o s s i b l e v a l u e s o f c .$
	Answered by ajfour last updated on 29/Sep/23

	$c = 3 ?$
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