document.write( "Question 1010315: find all other zeros give 2i is one zero.
\n" ); document.write( "f(x) = x^5 - 3x^4 + 5x^3 - 15x^2 + 4x - 12
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Algebra.Com's Answer #625820 by MathTherapy(10556)\"\" \"About 
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\n" ); document.write( "find all other zeros give 2i is one zero.
\n" ); document.write( "f(x) = x^5 - 3x^4 + 5x^3 - 15x^2 + 4x - 12
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One zero is 2i, so the other, its conjugate is: - 2i
\n" ); document.write( "This gives us: (x - 2i)(x + 2i), or \"x%5E2+%2B+4\"
\n" ); document.write( "Dividing \"x%5E5+-+3x%5E4+%2B+5x%5E3+-+15x%5E2+%2B+4x+-+12\" by \"x%5E2+%2B+4\" results in:
\n" ); document.write( "\"x%5E3+-+3x%5E2+%2B+x+-+3\", which can be factored into:
\n" ); document.write( "\"x%5E2%28x+-+3%29+%2B+1%28x+-+3%29\"
\n" ); document.write( "\"%28x%5E2+%2B+1%29%28x+-+3%29\"
\n" ); document.write( "\"%28x+%2B+i%29%28x+-+i%29%28x+-+3%29\".
\n" ); document.write( "This leads to zeroes of: - i, i, and 3.
\n" ); document.write( "Thus the zeroes of \"f%28x%29+=+x%5E5+-+3x%5E4+%2B+5x%5E3+-+15x%5E2+%2B+4x+-+12\" are: \"highlight_green%28system%28x+=%22+%22%2B-+2i%2C+x+=%22+%22+%2B-i%2C+x+=+3%29%29\" \n" ); document.write( "
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