document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=64642>Question 64642</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am struggling with some problems. Could someone please help me!!!!\r<BR>\n" );
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document.write( "1. Find a third degree polynomial with real coefficents and with real zeros 2 and 4+i. Write your answer in ax^3+bx^2+cx+d form. I have x^3-10x^2+33x-34 is that correct and is there anything else I should do to it?\r<BR>\n" );
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document.write( "2. Use Decartes' Rule of Sign to find the number of possible number of positive zeros and the possible number of negative zeros of Q(x)= x^4-2x^3+4x^2-3x-2. I am completely stuck on this one and don't even know where to start.\r<BR>\n" );
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document.write( "Thank you for your help!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #46237 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=46237\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I am struggling with some problems. Could someone please help me!!!! <BR>\n" );
document.write( "1. Find a third degree polynomial with real coefficents and with real zeros 2 and 4+i. Write your answer in ax^3+bx^2+cx+d form. I have x^3-10x^2+33x-34 is that correct and is there anything else I should do to it? <BR>\n" );
document.write( "SINCE COEFFICIENTS ARE REAL ,THEN COMPLEX ROOTS SHOULD BE IN CONJUGATES.<BR>\n" );
document.write( "HENCE IF 4+i IS A ROOT,THEN 4-i SHOULD ALSO BE A ROOT.<BR>\n" );
document.write( "HENCE THE 3 ROOTS ARE 2,4+i,4-i.HENCE POLYNOMIAL IS <BR>\n" );
document.write( "(X-2)[X-(4+i)][X-(4-i)]=0<BR>\n" );
document.write( "(X-2)[(X-4)^2-i^2]=0<BR>\n" );
document.write( "(X-2)[X^2-8X+16+1]=0<BR>\n" );
document.write( "X^3 - 8X^2+17X-2X^2+16X-34=0<BR>\n" );
document.write( "X^3-10X^2+33X-34=0...........OK\r<BR>\n" );
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document.write( "2. Use Decartes' Rule of Sign to find the number of possible number of positive zeros and the possible number of negative zeros of Q(x)= x^4-2x^3+4x^2-3x-2. I am completely stuck on this one and don't even know where to start. <BR>\n" );
document.write( "THE RULE SAYS.FIND CHANGES IN SIGN OF COEFFICIENTS OF THE TERMS OF THE FUNCTION WHEN WRITTEN IN A DESCENDING ORDER.<BR>\n" );
document.write( "WE ALREADY HAVE THE FUNCTION IN DECENDING ORDER.<BR>\n" );
document.write( "WE HAVE HERE ONE CHANGE FROM +1 TO -2<BR>\n" );
document.write( "2 ND CHANGE FROM -2 TO +4<BR>\n" );
document.write( "3 RD. CHANGE FROM +4 TO -3<BR>\n" );
document.write( "SO THE NUMBER OF CHANGES =3 = MAXIMUM NUMBER OF POSITIVE RATIONAL ROOTS.THEY COULD BE 3 OR 3-2 = 1.\r<BR>\n" );
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document.write( "Thank you for your help!!!!<BR>\n" );
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