document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=571036>Question 571036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For a polynomial f(x) with real coefficients having given the degree and zeros.\r<BR>\n" );
document.write( "\n" );
document.write( "Degree 4; zeros:-2-5i; 5 multiplicity 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #367951 by </B><A HREF=/tutors/aboutme.mpl?userid=reviewermath><B>reviewermath(1029)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=reviewermath><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=reviewermath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=367951\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The conjugate of -2-5i is -2+5i. We first get a quadratic equation having -2-5i and -2+5i as roots.<BR>\n" );
document.write( "sum = (-2-5i) + (-2+5i) = -4<BR>\n" );
document.write( "product = (-2-5i)(-2+5i) = 29<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-+%28sum%29x+%2B+product+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-+%28sum%29x+%2B+product+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The quadratic equation is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4x+%2B+29+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x+%2B+29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Next, we get the quadratic equation having 5 as a double root.\r<BR>\n" );
document.write( "\n" );
document.write( "The quadratic equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2+=+0 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "We multiply the two quadratic equations to get the polynomial of degree 4.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+%2B+4x+%2B+29%29%2A%28x-5%29%5E2+=+0 ALIGN=MIDDLE  ALT=\"%28x%5E2+%2B+4x+%2B+29%29%2A%28x-5%29%5E2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+-6x%5E3+%2B14x%5E2+-190x+%2B+725+=+0 ALIGN=MIDDLE  ALT=\"x%5E4+-6x%5E3+%2B14x%5E2+-190x+%2B+725+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+-6x%5E3+%2B14x%5E2+-190x+%2B+725+=+0 ALIGN=MIDDLE  ALT=\"x%5E4+-6x%5E3+%2B14x%5E2+-190x+%2B+725+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );