document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178991>Question 1178991</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that the roots of 2𝑥<BR>\n" );
document.write( "2 + (1 − 2𝑛)𝑥 − 𝑛 = 0 are rational and <BR>\n" );
document.write( "unequal if 𝑛 is an integer. </SPAN>\n" );
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document.write( " 2𝑥^2 + (1 − 2𝑛)𝑥 − 𝑛 = 0 \r<BR>\n" );
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document.write( "comparing the equation with ax^2 +bx +c\r<BR>\n" );
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document.write( "a= 2,  b=(1-2n), c=-n\r<BR>\n" );
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document.write( "b^2 = (1-2n)^2 <BR>\n" );
document.write( "1-4n +4n^2\r<BR>\n" );
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document.write( "4ac = (4)(2)(-n)<BR>\n" );
document.write( "= -8n<BR>\n" );
document.write( "b^2 -4ac<BR>\n" );
document.write( "1-4n +4n^2 -(-8n)<BR>\n" );
document.write( "4n^2 -3n +1<BR>\n" );
document.write( "4n^2+4n+1<BR>\n" );
document.write( "(2n+1)^2<BR>\n" );
document.write( "For all values of n, (2n+1)^2 >0<BR>\n" );
document.write( "Therefore roots are real and unequal\r<BR>\n" );
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document.write( " </SPAN>\n" );
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