document.write( "Question 29538: how do you determine an equation from the zeros\r
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Algebra.Com's Answer #16314 by AnlytcPhil(1810)\"\" \"About 
You can put this solution on YOUR website!
how do you determine an equation from the zeros \r\n" );
document.write( "for example \r\n" );
document.write( "-3/4, 2/5 \r\n" );
document.write( "-4+2(square root)3\r\n" );
document.write( "-4-2(square root)3 \r\n" );
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document.write( "To find a polynomial equation whose zeros are r1, r2, r3, r4, form the \r\n" );
document.write( "following equation, multiply it out and simplify it.\r\n" );
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document.write( "(x - r1)(x - r2)(x - r3)(x - r4) = 0\r\n" );
document.write( "                            _          _\r\n" );
document.write( "For r1=-3/4, r2=2/3, r3=-4+2Ö3, r4=-4-2Ö3)\r\n" );
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document.write( "Such an equation would be:\r\n" );
document.write( "                             _             _ \r\n" );
document.write( "(x + 3/4)(x - 2/5)[x - (-4+2Ö3)][x - (-4-2Ö3)] = 0\r\n" );
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document.write( "Multiply that out -- a very big job -- then you'll get\r\n" );
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document.write( "x4 + (167/20)x3 + (13/2)x2 - x - 6/5 = 0\r\n" );
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document.write( "Clearing of fractions\r\n" );
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document.write( "20x4 + 167x3 + 130x2 - 20x - 24 = 0\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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