Aryang
prove that
x^8 -x^7 + x^2 -x +15 has no real root
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mukushla
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for \(x\le0\) its obvious that \(x^8 -x^7 + x^2 -x +15 >0\)
u just prove for \(x>0\) : \(x^8 -x^7 + x^2 -x +15 >0\)
Aryang
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and does descartes' theorem help a great deal ?
according to that,,it should have max 4 +ve roots..
mukushla
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no need to descartes...
Aryang
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well what then ?
Aryang
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ohh wait,,leme try..
mukushla
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well just show that \(x^8 -x^7 + x^2 -x +15>0\) for every real number
Yahoo!
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descartes helps a lot lol
Aryang
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for x>1 ,,
x^8 > x^7 and x^2 >x
so f(x) > 0 for x>1
for 0<x<1 ,
x> x^2 > x^7 > x^8
we then have 15 - (fraction + fraction) ,,which is obviously >0
so f(x) is always >0
am i right ?
mukushla
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exactly
Aryang
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ohh..thank you @mukushla
your little hint only helped me a lot :)
mukushla
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np...:)