document.write( "Question 765788: I am having trouble with learning polynomials. Please help me.\r
\n" ); document.write( "\n" ); document.write( "Find the complex zeros of the polynomial function. Write f in factored form.\r
\n" ); document.write( "\n" ); document.write( "f(x)= x^4 + 12x^3 - 9x^2 + 48x - 52\r
\n" ); document.write( "\n" ); document.write( "The complex zeros of f are: ?
\n" ); document.write( "Use the complex zeros to write f in factored form: f(x) = ? \n" ); document.write( "

Algebra.Com's Answer #466424 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"f%28x%29=+x%5E4+%2B+12x%5E3+-+9x%5E2+%2B+48x+-+52\"$ ..write $\"-+9x%5E2\"$ as $\"-+13x%5E2%2B4x%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E4%2B12x%5E3-13x%5E2%2B4x%5E2%2B48x-52\"$ ....group\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%5E4%2B4x%5E2%29%2B%2812x%5E3%2B48x%29-%2813x%5E2%2B52%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=x%5E2%28x%5E4%2B4%29%2B12x%28x%5E2%2B4%29-13%28x%5E2%2B4%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%5E2%2B12x-13%29+%28x%5E2%2B4%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x%5E2%2B13x-1x-13%29+%28x%5E2%2B4%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%28x-1%29+%28x%2B13%29%28x%5E2%2B4%29\"$ \r
\n" ); document.write( "\n" ); document.write( "so, to find zeros use zero product rule:\r
\n" ); document.write( "\n" ); document.write( " $\"%28x-1%29+%28x%2B13%29%28x%5E2%2B4%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"x-1=0\"$ => $\"x=1\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"x%2B13=0\"$ => $\"x=-13\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"x%5E2%2B4=0\"$ => $\"x=sqrt%28-4%29\"$ => $\"x=2i\"$ or => $\"x=-2i\"$ \r
\n" ); document.write( "\n" ); document.write( "so, your solutions are: $\"x=1\"$ , $\"x=-13\"$ (real), $\"x=2i\"$ , and $\"x=-2i\"$ (complex)\r
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