document.write( "Question 848747: write polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros
\n" ); document.write( "2, i, -i \n" ); document.write( "

Algebra.Com's Answer #511259 by josgarithmetic(39620) $\"\"$ $\"About$

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Degree three, because you want exactly those three given roots. I will do this only part-way:\r
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\n" ); document.write( "\n" ); document.write( "The binomial factors of f will be $\"%28x-2%29%28x-i%29%28x-%28-i%29%29\"$ . Multiply the two imaginary factors first:
\n" ); document.write( " $\"%28x-i%29%28+x-%28-1%29%29\"$
\n" ); document.write( " $\"%28x-i%29%28x%2Bi%29\"$
\n" ); document.write( " $\"x%5E2-i%5E2\"$
\n" ); document.write( " $\"x%5E2-%28-1%29\"$
\n" ); document.write( " $\"x%5E2%2B1\"$
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\n" ); document.write( "So revise the function expression as $\"%28x-2%29%28x%5E2%2B1%29\"$
\n" ); document.write( "... and you can finish the rest. \n" ); document.write( "

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