document.write( "Question 1168782: prove that if the sum of the sequence of the roots of the equation ax^2+bx+c=0 is 1 then b^2=2ac=a^2 \n" ); document.write( "
Algebra.Com's Answer #793481 by ikleyn(52797)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "prove that if the sum of the sequence of the roots of the equation ax^2+bx+c=0 is 1 then b^2=2ac=a^2
\n" ); document.write( "~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            Let's check if the statement of the post is valid.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "Let's consider the equation\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    x*(x-1) = 0,  or,  equivalently,  x^2 - x = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It has the roots  x= 0  and  x= 1;  the sum of the roots is 1,  which is in accordance with the description.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The coefficients of the standard form equation are  a = 1, b = -1, c = 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The statement asserts that  a^2 = b^2, and it is true.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It asserts also that a^2 = 2ac, but it is  WRONG :  a^2 = 1, 2ac = 0  and 1 =/= 0.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus the problem' statement is  FALSE.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In other words, this \"quasi\"-problem is a  FAKE.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "----------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It seems to me,  that I see this problem not for the first time at this forum.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let me  AWARE  you,  that  -EITHER-  the source of the problem is  UNTRUSTED,  -OR-  you incorrectly reproduce it from the source.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "            - - - Or     B O T H - - - .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "In any case,  by posting it,  you  STOLE  the tutors'  valuable time.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If I see it next time at the forum,  I will delete it without any explanations.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "===========\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "At this spot,  a real problem from a real student could be placed,  who really needs my help and my attention.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "And during this time,  that I spent on your post  FOR  NOTHING,  I could help at least to two real students.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );