document.write( "Question 964458: find the complex zeros of the polynomial function f(x)=x^4+23x^2+22
\n" ); document.write( "write f in factored form f(x)=
\n" ); document.write( "please show step by step work i am very confused. \n" ); document.write( "

Algebra.Com's Answer #589350 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
here's how I would do it:
\n" ); document.write( " $\"+f%28x%29+=+x%5E4+%2B+23x%5E2+%2B+22+\"$
\n" ); document.write( "Let $\"+z+=+x%5E2+\"$
\n" ); document.write( "Substituting:
\n" ); document.write( " $\"+f%28x%29+=+z%5E2+%2B+23z+%2B+22+\"$
\n" ); document.write( "I can see that the factors for
\n" ); document.write( "finding roots
\n" ); document.write( " $\"+%28+z+%2B+22+%29%2A%28+z+%2B+1+%29+=+0+\"$
\n" ); document.write( "The solutions for $\"+Z+\"$ are:
\n" ); document.write( " $\"+z+=+-22+\"$
\n" ); document.write( " $\"+z+=+-1+\"$
\n" ); document.write( "------------------
\n" ); document.write( "So, now I can say:
\n" ); document.write( " $\"+x%5E2+=+-22+\"$
\n" ); document.write( " $\"+x%5E2+=+-1+\"$
\n" ); document.write( "-----------------
\n" ); document.write( " $\"+x+=+sqrt%2822%29%2Ai+\"$
\n" ); document.write( " $\"+x+=+-sqrt%2822%29%2Ai+\"$
\n" ); document.write( " $\"+x+=+i+\"$
\n" ); document.write( " $\"+x+=+-i+\"$
\n" ); document.write( "-------------
\n" ); document.write( "The 4 factors of $\"+f%28x%29+\"$ are:
\n" ); document.write( "

\n" ); document.write( "------------------------------------------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+%28+x+%2B+sqrt%2822%29%2Ai+%29%2A%28+x+-+sqrt%2822%29%2Ai+%29+\"$
\n" ); document.write( " $\"+x%5E2+%2B+22+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+%28+x+%2B+i+%29%2A%28+x+-+i+%29+=+x%5E2+%2B+1+%29+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+f%28x%29+=+%28+x%5E2+%2B+22+%29%2A%28+x%5E2+%2B+1+%29+\"$
\n" ); document.write( " $\"+f%28x%29+=+x%5E4+%2B+22x%5E2+%2B+x%5E2+%2B+22+\"$
\n" ); document.write( " $\"+f%28x%29+=+x%5E4+%2B+23x%5E2+%2B+22+\"$
\n" ); document.write( "OK\r
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\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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