Step 2 2004 q2Watch this thread
x^2 - α|x| + 2
= i^2 - 2|i| + 2
= -1 - 2(1) + 2
= -1 < 0
Hence there would exist a value
Solution below. Neither solution nor question mentions complex numbers. 2-a^2/4 is greater than 0 but if x is complex than (x-a/2)^2 could be negative so they haven't proved it would definitely give a number greater than 0.
How would I tell if context matters? This is a STEP 2 question which involves further maths content like complex numbers...
Being explicit, in this case the following observations are pretty much immediate:
(!) The variable name is x, rather than z, or w.
(2) There is no mention of complex numbers or anywhere in the question.
(3) The result is very obviously not true for complex numbers.
(4) The full question talks about intervals, which wouldn't make sense if x was allowed to be complex.
I'll grant you that the way is used might make you momentarily doubt whether you were supposed to working in rather than , but the deciding factor here would be that the question makes no sense under that assumption (due to (3) and (4)).