document.write( "Question 637985: find all the roots of f(x) = x^4-4x^3+6x^2-4x+5 if 2-i is one root \n" ); document.write( "
Algebra.Com's Answer #401986 by solver91311(24713)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "If is a zero, then is also a zero because complex zeros of polynomial functions always come in conjugate pairs.\r
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\n" ); document.write( "\n" ); document.write( "If is a zero of a polynomial function, then is a factor of the polynomial.\r
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\n" ); document.write( "\n" ); document.write( "So now you have two factors of the original polynomial:\r
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\n" ); document.write( "\n" ); document.write( "Multiply them using FOIL (treating the complex quantities as single values -- remember that the product of a pair of conjugates is the difference of two squares and that \r
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\n" ); document.write( "\n" ); document.write( "The result will be a quadratic trinomial. Use this as the divisor of the original 4th degree polynomial using polynomial long division. Click the link: Purple Math Polynomial Long Division if you need a refresher on this process.\r
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\n" ); document.write( "\n" ); document.write( "The quotient of the long division process will be a quadratic polynomial that is the product of the two remaining factors of the original polynomial. Use thee quadratic formula to determine the two remaining zeros.\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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