Find the sum of the roots, real and non-real, of the equation x2001+(12−x)2001=0, given that there are no multiple roots.
Find the sum of the roots, real and non-real, of the equation x2001+(12−x)2001=0,
given that there are no multiple roots.
x2001+(12−x)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)1x2000−x2001=0(20010)(12)2001−(20011)(12)2000x1+…+−(20011999)(12)2x1999+(20012000)(12)1x2000=0
(20012000)(12)1x2000−(20011999)(12)2x1999+−…+(20010)(12)2001=01000.5x2000−500250x1999+−…+(12)2001=0|:1000.5x2000−5002501000.5x1999+−…+(12)20011000.5=0x2000−500x1999+−…+(12)20011000.5=0x2000−500⏟=−2000∑k=1xkx1999+−…+(12)20011000.5=0
−2000∑k=1xk=−5002000∑k=1xk=500
The sum of the roots is 500
Find the sum of the roots, real and non-real, of the equation x2001+(12−x)2001=0,
given that there are no multiple roots.
x2001+(12−x)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)1x2000−x2001=0(20010)(12)2001−(20011)(12)2000x1+…+−(20011999)(12)2x1999+(20012000)(12)1x2000=0
(20012000)(12)1x2000−(20011999)(12)2x1999+−…+(20010)(12)2001=01000.5x2000−500250x1999+−…+(12)2001=0|:1000.5x2000−5002501000.5x1999+−…+(12)20011000.5=0x2000−500x1999+−…+(12)20011000.5=0x2000−500⏟=−2000∑k=1xkx1999+−…+(12)20011000.5=0
−2000∑k=1xk=−5002000∑k=1xk=500
The sum of the roots is 500