document.write( "Question 961971: I have 6 zeros, (x), (x-2), (x-5), (x-5), (x-7) and (x-9). How do I take these zeros and form them into a polynomial equation? \n" ); document.write( "

Algebra.Com's Answer #587719 by Edwin McCravy(20054) $\"\"$ $\"About$

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document.write( "(x), (x-2), (x-5), (x-5), (x-7) and (x-9) \r\n" );
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document.write( "are NOT zeros, they are FACTORS.\r\n" );
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document.write( "The zeros are \r\n" );
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document.write( "0, 2, 5, 5, 7, and 9.  \r\n" );
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document.write( "Since 5 is listed twice it is said to\r\n" );
document.write( "be a zero of multiplicity 2.\r\n" );
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document.write( "To find a polynomial with those zero, we start by setting \r\n" );
document.write( "x equal to each zero:\r\n" );
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document.write( "x=0, x=2, x=5, x=5, x=7, and x=9.  \r\n" );
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document.write( "Then we subtract the zero on the right from both sides of \r\n" );
document.write( "each of those 6 equations:\r\n" );
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document.write( "x-0=0, x-2=0, x-5=0, x-7=0, x-9=0\r\n" );
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document.write( "Then we use the principle that equals multiplied by equals gives\r\n" );
document.write( "equals.\r\n" );
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document.write( "So we multiply all the left sides together and all the right sides\r\n" );
document.write( "together.  (Multiplying all the right sides together just gives 0.)\r\n" );
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document.write( "(x-0)(x-2)(x-5)(x-5)(x-7)(x-9) = 0\r\n" );
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document.write( "And since x-0 is just x, we have\r\n" );
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document.write( "(x)(x-2)(x-5)(x-5)(x-7)(x-9) = 0\r\n" );
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document.write( "Those are the factors you gave.  But again, the zeros are\r\n" );
document.write( "0,2,5,5,7,9\r\n" );
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document.write( "And after lots of multiplication we end up with:\r\n" );
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document.write( "Therefore the polynomial that has those 6 zeros is\r\n" );
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document.write( "I purposely left out the coefficient of  because some\r\n" );
document.write( "teachers have complained that students have been just copying \r\n" );
document.write( "our answers and dishonestly turning them in for credit as though \r\n" );
document.write( "they had done the work themselves. \r\n" );
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document.write( "Edwin

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