document.write( "Question 467867: 11. Find the real and complex zeros of the following function. Please show all of your work.
\n" ); document.write( " f(x)=x³-2x²+16\r
\n" ); document.write( "\n" ); document.write( "please help. thank u! \n" ); document.write( "
Algebra.Com's Answer #321068 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
Find the real and complex zeros of the following function. Please show all of your work.
\n" ); document.write( "f(x)=x³-2x²+16
\n" ); document.write( "...
\n" ); document.write( "f(x)=x³-2x²+16
\n" ); document.write( "If you are allowed to use a graphing calculator you will find that the given function has only one rational real root=-2. I could have used the rational roots theorem, but I don't know how to show you the procedure with this format.
\n" ); document.write( "..
\n" ); document.write( "Divide f(x) by (x+2) by long division or by -2 using synthetic division. (again, this format doesn't allow me to show you how to do this)
\n" ); document.write( "..
\n" ); document.write( "(x³-2x²+16)/(x+2)=(x^2-4x+8)
\n" ); document.write( "f(x)=(x+2)(x^2-4x+8)
\n" ); document.write( "..
\n" ); document.write( "x^2-4x+8=0
\n" ); document.write( "completing the square
\n" ); document.write( "(x^2-4x+4)+8-4=0
\n" ); document.write( "(x-2)^2=-4
\n" ); document.write( "take sqrt of both sides
\n" ); document.write( "x-2=±√-4
\n" ); document.write( "x=2±√-4=2±2i
\n" ); document.write( "f(x)=(x+2)(2+2i)(2-2i)
\n" ); document.write( "This function has one real root and 2 imaginary roots \n" ); document.write( "
\n" );