document.write( "Question 1006071: If a, b, c are odd integers, then the equation ax2 + bx + c = 0 has no integer solution. \r
\n" ); document.write( "\n" ); document.write( "How can I prove this?\r
\n" ); document.write( "\n" ); document.write( "Sorry if its the wrong section >.< \n" ); document.write( "

Algebra.Com's Answer #622209 by ikleyn(52790) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "If a, b, c are odd integers, then the equation ax2 + bx + c = 0 has no integer solution.
\n" ); document.write( "-----------------------------------------------------------------\r
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Proof\r\n" );
document.write( "\r\n" );
document.write( "Write the equation in the form\r\n" );
document.write( "\r\n" );
document.write( " = .\r\n" );
document.write( "\r\n" );
document.write( "If x is even then the left side is even, while the right side is odd. Contradiction.\r\n" );
document.write( "\r\n" );
document.write( "If x is odd, then the left side is even, while the right side is odd. Contradiction again.\r\n" );
document.write( "\r\n" );
document.write( "Hence, the equation has no solution(s) under the given conditions.\r\n" );
document.write( "\r\n" );
document.write( "The proof is completed.\r\n" );
document.write( "

\n" ); document.write( " \n" ); document.write( "

\n" );