document.write( "Question 403541: Hello. I was hoping you could please help me?
\n" ); document.write( "I need to solve this equation : \r
\n" ); document.write( "\n" ); document.write( "k^5+4k^4-32k^3=0\r
\n" ); document.write( "\n" ); document.write( "Since its highest degree is 5, my teacher said we should get 5 roots, but when I tried it, I only got 3 roots, which were: 0, -8, and 4
\n" ); document.write( "Can you please show me the correct way to do it? I'm doing it by factoring... \n" ); document.write( "

Algebra.Com's Answer #285406 by richard1234(7193) $\"\"$ $\"About$

You can put this solution on YOUR website!
There's a nice theorem (fairly difficult to prove though) called the fundamental theorem of algebra that says that any n-degree polynomial has n complex roots, including multiple roots. Therefore we expect five roots.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Factoring the expression, this becomes\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"k%5E3%28k%5E2+%2B+4k+-+32%29+=+0\"$ --> $\"k%5E3+=+0\"$ or $\"k%5E2+%2B+4k+-+32+=+0\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The first equation has a triple root of 0. The second equation can be factored as $\"%28x+%2B+8%29%28x+-+4%29+=+0\"$ --> x = -8, x = 4. \n" ); document.write( "

\n" );