document.write( "Question 1195204: Solve these two equations:\r
\n" ); document.write( "\n" ); document.write( "(a) The quadratic equation \"2ax%5E2-4ax%2Ba%2B1=0\" has two roots. If one root is five times the other, what is the value of a?\r
\n" ); document.write( "\n" ); document.write( "(b) If \"x%2B2\" and \"x-3\" are factors of the polynomial \"p%28x%29+=+x%5E3%2B5x%5E2%2Bax%2Bb\", find \"a\". \n" ); document.write( "
Algebra.Com's Answer #827729 by MathTherapy(10555)\"\" \"About 
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Solve these two equations:\r
\n" ); document.write( "\n" ); document.write( "(a) The quadratic equation \"2ax%5E2-4ax%2Ba%2B1=0\" has two roots. If one root is five times the other, what is the value of a?\r
\n" ); document.write( "\n" ); document.write( "(b) If \"x%2B2\" and \"x-3\" are factors of the polynomial \"p%28x%29+=+x%5E3%2B5x%5E2%2Bax%2Bb\", find \"a\".
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\"matrix%281%2C3%2C+2ax%5E2+-+4ax+%2B+a+%2B+1%2C+%22=%22%2C+0%29\" =====> \"matrix%281%2C4%2C+%282a%29x%5E2+%28-+4a%29x%2C+%22+%2B%28a+%2B+1%29%22%2C+%22=%22%2C+0%29\"\r\n" );
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document.write( "Let smaller root be R\r\n" );
document.write( "Then larger root = 5R\r\n" );
document.write( "Sum of the roots, or . Also, sum of roots = R + 5R = 6R.\r\n" );
document.write( "                                  Therefore, \r\n" );
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document.write( "Product of the roots, or \"matrix%281%2C5%2C+p%2C+%22=%22%2C+c%2Fa%2C+%22=%22%2C+%28a+%2B+1%29%2F%282a%29%29\". Also, product of roots = R(5R) = 5R2 = \"matrix%281%2C5%2C+5%281%2F3%29%5E2%2C+%22=%22%2C+5%281%2F9%29%2C+%22=%22%2C+5%2F9%29\" \r\n" );
document.write( "                       Therefore, \"matrix%281%2C3%2C+%28a+%2B+1%29%2F%282a%29%2C+%22=%22%2C+5%2F9%29\"\r\n" );
document.write( "                                     10a = 9(a + 1)----- Cross-multiplying\r\n" );
document.write( "                                     10a = 9a + 9\r\n" );
document.write( "                                10a - 9a = 9\r\n" );
document.write( "                                      \"highlight_green%28matrix%281%2C3%2C+a%2C+%22=%22%2C+9%29%29\"\r\n" );
document.write( "***BTW, this is Part (a).
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