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Find the sum of the roots, real and non-real, of the equation x2001+(12x)2001=0, given that there are no multiple roots.

 Jun 20, 2019

Best Answer 

 #1
avatar+26397 
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Find the sum of the roots, real and non-real, of the equation x2001+(12x)2001=0,
given that there are no multiple roots.

 

x2001+(12x)2001=0x2001+(20010)(12)2001(20011)(12)2000x1++(20011999)(12)2x1999+(20012000)(12)1x2000(20012001)x2001=0x2001+(20010)(12)2001(20011)(12)2000x1++(20011999)(12)2x1999+(20012000)(12)1x2000x2001=0(20010)(12)2001(20011)(12)2000x1++(20011999)(12)2x1999+(20012000)(12)1x2000=0

 

(20012000)(12)1x2000(20011999)(12)2x1999++(20010)(12)2001=01000.5x2000500250x1999++(12)2001=0|:1000.5x20005002501000.5x1999++(12)20011000.5=0x2000500x1999++(12)20011000.5=0x2000500=2000k=1xkx1999++(12)20011000.5=0

 

2000k=1xk=5002000k=1xk=500

 

The sum of the roots is 500

 

laugh

 Jun 20, 2019
 #1
avatar+26397 
+3
Best Answer

Find the sum of the roots, real and non-real, of the equation x2001+(12x)2001=0,
given that there are no multiple roots.

 

x2001+(12x)2001=0x2001+(20010)(12)2001(20011)(12)2000x1++(20011999)(12)2x1999+(20012000)(12)1x2000(20012001)x2001=0x2001+(20010)(12)2001(20011)(12)2000x1++(20011999)(12)2x1999+(20012000)(12)1x2000x2001=0(20010)(12)2001(20011)(12)2000x1++(20011999)(12)2x1999+(20012000)(12)1x2000=0

 

(20012000)(12)1x2000(20011999)(12)2x1999++(20010)(12)2001=01000.5x2000500250x1999++(12)2001=0|:1000.5x20005002501000.5x1999++(12)20011000.5=0x2000500x1999++(12)20011000.5=0x2000500=2000k=1xkx1999++(12)20011000.5=0

 

2000k=1xk=5002000k=1xk=500

 

The sum of the roots is 500

 

laugh

heureka Jun 20, 2019

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