document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254301>Question 254301</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I actually have three questions. Two of the same type. Different numbers of roots, and I'm not even sure this is the right heading, but I couldn't find one that fit better, if you could help that would be great. If they're the same thing in the end, one being solved is fine, I just need a better explanation than the notes I was given for my online class. :(. The third question has imaginary numbers in it, and after a failed, and very irritating attempt I thought I would seek assistance.\r<BR>\n" );
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document.write( "1. Determine all roots of P(x) = 3x^4+5x^3-9x^2-10x+8.\r<BR>\n" );
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document.write( "2. Determine all the roots of P(x) = 3x^5+5x^4+10x^3+14x^2+3x-3.\r<BR>\n" );
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document.write( "3. Determine a polynomial P(x) with real coefficients and of degree 5 for which three of its roots are x= -1, x = 1+2i and x= -3i.\r<BR>\n" );
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document.write( "Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #186670 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=186670\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Determine all roots of P(x) = 3x^4+5x^3-9x^2-10x+8.<BR>\n" );
document.write( "I had to graph it to find zeroes:<BR>\n" );
document.write( "x = 1.6371972...<BR>\n" );
document.write( "x = -2.409123<BR>\n" );
document.write( "The other two roots seem to be complex.<BR>\n" );
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document.write( "2. Determine all the roots of P(x) = 3x^5+5x^4+10x^3+14x^2+3x-3.<BR>\n" );
document.write( "x = 1/3 is the only Real root<BR>\n" );
document.write( "The other 4 roots seem to be complex.<BR>\n" );
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document.write( "3. Determine a polynomial P(x) with real coefficients and of degree 5 for which three of its roots are x= -1, x = 1+2i and x= -3i. <BR>\n" );
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document.write( "Since the coefficients are Real x = 1-2i and x = +3i<BR>\n" );
document.write( "are also roots<BR>\n" );
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document.write( "P(x) = (x+1)((x-1)-2i)((x-1)+2i)(x-3i)(x+3i)<BR>\n" );
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document.write( "P(x) = (x+1)((x-1)^2+4)(x^2+9)<BR>\n" );
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document.write( "P(x) = (x+1)(x^2-2x+5)(x^2+9)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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