document.write( "Question 825428: Write a polynomial function F of the least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. \r
\n" ); document.write( "\n" ); document.write( "1) $\"1-+sqrt%285%29\"$ \r
\n" ); document.write( "\n" ); document.write( "2) $\"+sqrt+%282%29\"$ , 3i \n" ); document.write( "

Algebra.Com's Answer #497303 by josgarithmetic(39618) $\"\"$ $\"About$

You can put this solution on YOUR website!
Initial impression here is that the irrational root would be treated similarly to the imaginary root. The help I give here is for question #1.\r
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\n" ); document.write( "\n" ); document.write( " $\"%281-sqrt%285%29%29%281%2Bsqrt%285%29%29=1%5E2-%28sqrt%285%29%29%5E2\"$
\n" ); document.write( " $\"1-5=-4\"$ \r
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\n" ); document.write( "\n" ); document.write( "Hoping to use that,
\n" ); document.write( " $\"F=%28x-%281-sqrt%285%29%29%29%28x-%281%2Bsqrt%285%29%29%29\"$
\n" ); document.write( " $\"%28x-1%2Bsqrt%285%29%29%28x-1-sqrt%285%29%29\"$
\n" ); document.write( " $\"%28x-1%29%5E2-%28sqrt%285%29%29%5E2\"$
\n" ); document.write( " $\"x%5E2-2x%2B1-5\"$
\n" ); document.write( " $\"x%5E2-2x-4\"$ \r
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\n" ); document.write( "\n" ); document.write( "There it is!
\n" ); document.write( " $\"highlight%28F=x%5E2-2x-4%29\"$ , and the TWO roots are $\"1-sqrt%285%29\"$ and $\"1%2Bsqrt%285%29\"$ . \n" ); document.write( "

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