document.write( "Question 363587: I am suppose to find the number of real zeros and the number of imaginary zeros for the polynomial.\r
\n" ); document.write( "\n" ); document.write( "x^4+4x^3+5x^2+4x+4=f(X)\r
\n" ); document.write( "\n" ); document.write( "The answers I got were 1 real zero and 3 imaginary zeros? \n" ); document.write( "
Algebra.Com's Answer #259268 by vasumathi(46)\"\" \"About 
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Solution: Let x = -2 .Plug in this in the given polynomial\r
\n" ); document.write( "\n" ); document.write( "x^4+4x^3+5x^2+4x+4
\n" ); document.write( "(-2)^4 + 4 (-2)^3+5(-2)^2 +4(-2)+ 4=16-32+20-8+4=0
\n" ); document.write( "so x = -2 is a root and (x+2) is a factor
\n" ); document.write( "Let us divide the given polynomial with (x+2)
\n" ); document.write( "we get
\n" ); document.write( "x^3+2x^2+x+2
\n" ); document.write( "again plug in x = -2
\n" ); document.write( "so (x+2) is a factor again and divide x^3+2x^2+x+2 by (x+2)
\n" ); document.write( "we get x^2 + 1 after division
\n" ); document.write( "and the roots of x^2 +1 = 0 are x = + i and x = -i
\n" ); document.write( "so the roots are \r
\n" ); document.write( "\n" ); document.write( "x = -2 repeated twice
\n" ); document.write( "so there are two real roots
\n" ); document.write( "-2 and -2
\n" ); document.write( "and there are two complex roots .They are i and -i
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