document.write( "Question 269865: I need help on finding the potential rational zeros of the polynomial function
\n" ); document.write( "f(x) = -4x^4 + 3x^2 - 4x + 6 \n" ); document.write( "
Algebra.Com's Answer #197703 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
need help on finding the potential rational zeros of the polynomial function
\n" ); document.write( "f(x) = -4x4 + 3x2 - 4x + 6
\n" ); document.write( "
\r\n" );
document.write( "All rational zeros of a polynomial in descending order, \r\n" );
document.write( "if there are any, are fractions with a numerator which \r\n" );
document.write( "is ± an integer factor of the last term in absolute value,\r\n" );
document.write( "and a denominator which is ± an integer factor of the first \r\n" );
document.write( "coefficient in absolute value.\r\n" );
document.write( "\r\n" );
document.write( "The factors of the last term, 6, in absolute value are\r\n" );
document.write( "\r\n" );
document.write( "1, 2, 3, 6 \r\n" );
document.write( "\r\n" );
document.write( "The factors of the first coefficient, -4, in absolute value\r\n" );
document.write( "are\r\n" );
document.write( "\r\n" );
document.write( "1,2,4.\r\n" );
document.write( "\r\n" );
document.write( "No we make all possible fractions which have a numerator \r\n" );
document.write( "of 1,2,3,or 6 and a denominator 1,2, or 4:\r\n" );
document.write( "\r\n" );
document.write( "1/1, 1/2, 1/4, 2/1, 2/2. 2/4, 3/1, 3/2. 3/4, 6/1, 6/2, 6/4\r\n" );
document.write( "\r\n" );
document.write( "Now we reduce them all\r\n" );
document.write( "\r\n" );
document.write( "1, 1/2, 1/4, 2, 1. 1/2, 3, 3/2. 3/4, 6, 3, 3/2\r\n" );
document.write( "\r\n" );
document.write( "Now we remove the duplications:\r\n" );
document.write( "\r\n" );
document.write( "1, 1/2, 1/4, 2, 3, 3/2, 3/4, 6.\r\n" );
document.write( "\r\n" );
document.write( "Now we put ± beside them all:\r\n" );
document.write( "\r\n" );
document.write( "±1, ±1/2, ±1/4, ±2, ±3, ±3/2, ±3/4, ±6.\r\n" );
document.write( "\r\n" );
document.write( "If there are any rational zeros, they are among\r\n" );
document.write( "these 16.  \r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );