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asianism
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asianism
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asianism
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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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robertgallacher
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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
x^2 - α|x| + 2
= i^2 - 2|i| + 2
= -1 - 2(1) + 2
= -1 < 0
Hence there would exist a value
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DFranklin
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#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.
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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asianism
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#6
(Original post by DFranklin)
Context matters. x is obviously intended to be real here.
Context matters. x is obviously intended to be real here.
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DFranklin
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#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...
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

(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



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