document.write( "Question 729707: a)Find a 5th degreed polynomial with roots x=2, x=2+i and x=1-i.
\n" ); document.write( "b)Now find the particular polynomial with the given roots in part a. that passes through (0,-60). \n" ); document.write( "

Algebra.Com's Answer #446247 by josgarithmetic(39799) $\"\"$ $\"About$

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The two complex roots with imaginary components require two additional complex roots, the conjugates.\r
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\n" ); document.write( "\n" ); document.write( "Along with (x-2), (x-(2+i)) makes (x-(2-i)) also necessary.
\n" ); document.write( "(x-(1-i)) makes (x-(1+i)) also necessary. \r
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\n" ); document.write( "\n" ); document.write( "The complex pairs can be turned into quadratic factors this way:
\n" ); document.write( " $\"%28x-%282%2Bi%29%29+%2A+%28x-%282-i%29%29=x%5E2-4x%2B5\"$ ;
\n" ); document.write( " $\"%28x-%281-i%29%29+%2A+%28x-%281%2Bi%29%29=x%5E2-2x%2B2\"$ .\r
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\n" ); document.write( "\n" ); document.write( "A function with the five expected roots may be
\n" ); document.write( " $\"highlight%28p%28x%29=%28x-2%29%28x%5E2-4x%2B5%29%28x%5E2-2x%2B2%29%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Your next objective was to use that function as a starting relation to find a function to the degree 5 (?) which contains the point (0, -60). You may possibly need a constant factor with the polynomial to be able to have the function value equal to -60. Letting x=0 is simple; do this and then carry out the remaining multiplications.\r
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\n" ); document.write( "\n" ); document.write( " $\"-60=%280-2%29%280-0%2B5%29%280-0%2B2%29%2Ak\"$ , where k is some constant factor in case the original factors do not give -60.
\n" ); document.write( "By intent, I have not finished this work but it should be very easy. \n" ); document.write( "

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