# Step 2 2004 q2

#1
Is this question only true when x is not a complex number?
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#2
question below
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#3
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.
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1 year ago
#4
Yes, eg. x=i, α=2

x^2 - α|x| + 2
= i^2 - 2|i| + 2
= -1 - 2(1) + 2
= -1 < 0

Hence there would exist a value
1
1 year ago
#5
(Original post by asianism)
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.
Context matters. x is obviously intended to be real here.
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#6
(Original post by DFranklin)
Context matters. x is obviously intended to be real here.
How would I tell if context matters? This is a STEP 2 question which involves further maths content like complex numbers...
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1 year ago
#7
(Original post by asianism)
How would I tell if context matters? This is a STEP 2 question which involves further maths content like complex numbers...
Well, context *always* matters, even if usually it's obvious enough that no-one remarks on it.
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)).
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