document.write( "Question 626148: Use the given zero, 5i, to find all the zeros of the function: f(x)=2x^3+3x^2+50x+75 \n" ); document.write( "

Algebra.Com's Answer #394009 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
The complex zeros always come in pairs that
\n" ); document.write( "look like $\"+a+%2B+b%2Ai+\"$ and $\"+a+-+b%2Ai+\"$ , so the
\n" ); document.write( "pairs of factors are $\"+x+-+5%2Ai+\"$ and $\"+x+%2B+5%2Ai+\"$
\n" ); document.write( "If I multiply these, I get $\"+x%5E2+-+25%2A%28-1%29+=+x%5E2+%2B+25+\"$
\n" ); document.write( "------------
\n" ); document.write( "Now I divide $\"+2x%5E3+%2B+3x%5E2+%2B+50x+%2B+75+\"$
\n" ); document.write( "by $\"+x%5E2+%2B+25+\"$ and I get $\"+2x+%2B+3+\"$ as the
\n" ); document.write( "3rd factor . Set it equal to zero.
\n" ); document.write( " $\"+2x+%2B+3+=+0+\"$
\n" ); document.write( " $\"+2x+=+-3+\"$
\n" ); document.write( " $\"+x+=+-%283%2F2%29+\"$
\n" ); document.write( "Here's the plot:
\n" ); document.write( " $\"+graph%28+500%2C+500%2C+-10%2C+10%2C+-200%2C+200%2C+2x%5E3+%2B+3x%5E2+%2B+50x+%2B+75+%29+\"$ \n" ); document.write( "

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