Županijsko natjecanje 2012 SŠ4 3
Dodao/la:
arhiva2. travnja 2012. Neka su
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i
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realni brojevi. Graf funkcije
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siječe koordinatne osi u tri različite točke
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,
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i
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. Dokaži da kružnica opisana trokutu
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siječe os
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u točki s ordinatom
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.
%V0
Neka su $p$ i $q$ realni brojevi. Graf funkcije $f(x)=x^2+px+q$ siječe koordinatne osi u tri različite točke $A$, $B$ i $C$. Dokaži da kružnica opisana trokutu $ABC$ siječe os $y$ u točki s ordinatom $1$.
Izvor: Županijsko natjecanje iz matematike 2012