document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=34922>Question 34922</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have been on this for hours, if any one can please direct me.\r<BR>\n" );
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document.write( "A polynomial f(t) of degree 3 satisfies f(&#8722;2) = 0, f(2) = 4, f'(&#8722;1) = 2, and f'(1) = &#8722;6.\r<BR>\n" );
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document.write( "(a) Write the general form of the polynomial and its derivative.\r<BR>\n" );
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document.write( "(b) Find four linear equations that must be satisfied by the unknown coefficients in the polynomial.\r<BR>\n" );
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document.write( "(c) Write the augmented matrix for your system of equations in (b) and row-reduce. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #21135 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=21135\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I have been on this for hours, if any one can please direct me.<BR>\n" );
document.write( "A polynomial f(t) of degree 3 satisfies f(&#8722;2) = 0, f(2) = 4, f'(&#8722;1) = 2, and f'(1) = &#8722;6.<BR>\n" );
document.write( "(a) Write the general form of the polynomial and its derivative.<BR>\n" );
document.write( "(b) Find four linear equations that must be satisfied by the unknown coefficients in the polynomial.<BR>\n" );
document.write( "(c) Write the augmented matrix for your system of equations in (b) and row-reduce.<BR>\n" );
document.write( " THE GENERAL FORM OF POLYNOMIAL OF DEGREE 3 IS<BR>\n" );
document.write( "F(T)= AT^3+BT^2+CT+D ....................EQN.A<BR>\n" );
document.write( "DF/DT= 3AT^2+2BT+C...................EQN.B<BR>\n" );
document.write( "WE ARE GIVEN F(-2)=0...SO SUBSTITUTING IN EQN.A<BR>\n" );
document.write( "-8A+4B-2C+D=0.............................EQN.I<BR>\n" );
document.write( "F(2)=4...SO SUBSTITUTING IN EQN.A<BR>\n" );
document.write( "8A+4B+2C+D=4................................EQN.II<BR>\n" );
document.write( "F'(-1)=2...SO SUBSTITUTING IN EQN.B<BR>\n" );
document.write( "3A-2B+C=2......................................EQN.III<BR>\n" );
document.write( "F'(1)=-6...SO SUBSTITUTING IN EQN.B<BR>\n" );
document.write( "3A+2B+C=-6..................................EQN.IV<BR>\n" );
document.write( "AUGMENTED MATRIX A IS <BR>\n" );
document.write( "-8,4,-2,1,0<BR>\n" );
document.write( "8,4,2,1,4<BR>\n" );
document.write( "3,-2,1,0,2<BR>\n" );
document.write( "3,2,1,0,-6<BR>\n" );
document.write( "I HOPE YOU CAN REDUCE THIS NOW AS YOU WANTED DIRECTION ...IF IN DOUBT SEE FOLLOWING EXAMPLE TO KNOW THE METHOD.<BR>\n" );
document.write( "----------------------------------------------------------------------<BR>\n" );
document.write( "The problem:<BR>\n" );
document.write( "2x-5y+ ___=-22<BR>\n" );
document.write( "__+y+3z=10<BR>\n" );
document.write( "x+___+8z=15<BR>\n" );
document.write( "The underscores represents blanks or O<BR>\n" );
document.write( "If this had to be an augmented matrix, how would I do that and get those variables?<BR>\n" );
document.write( "1 solutions<BR>\n" );
document.write( "Answer 20202 by venugopalramana(1462) About Me on 2006-04-16 22:01:33 (Show Source):<BR>\n" );
document.write( "2x-5y+ ___=-22...........................I<BR>\n" );
document.write( "__+y+3z=10.....................II<BR>\n" );
document.write( "x+___+8z=15...........................III<BR>\n" );
document.write( "2*EQN.III-EQN.I<BR>\n" );
document.write( "2X+16Z-2X+5Y=30+22=52<BR>\n" );
document.write( "5Y+16Z=52...........................IV<BR>\n" );
document.write( "EQN.IV-5*EQN.II<BR>\n" );
document.write( "5Y+16Z-5Y-15Z=52-50=2<BR>\n" );
document.write( "Z=2....SUBSTITUTING IN EQN.III<BR>\n" );
document.write( "X+8*2=15<BR>\n" );
document.write( "X=15-16=-1<BR>\n" );
document.write( "SUBSTITUTING FOR Z IN EQN.II<BR>\n" );
document.write( "Y+3*2=10<BR>\n" );
document.write( "Y=10-6=4<BR>\n" );
document.write( "USING MATRIX METHOD...AUGMENTED MATRIX IS<BR>\n" );
document.write( "2 -5 0 -22 1 0 0 ?<BR>\n" );
document.write( "0 1 3 10 0 1 0 ?<BR>\n" );
document.write( "1 0 8 15 0 0 1 ?<BR>\n" );
document.write( "NR1=R1/2<BR>\n" );
document.write( "1 -2.5 0 -11<BR>\n" );
document.write( "0 1 3 10<BR>\n" );
document.write( "1 0 8 15<BR>\n" );
document.write( "NR3=R3-R1<BR>\n" );
document.write( "1 -2.5 0 -11<BR>\n" );
document.write( "0 1 3 10<BR>\n" );
document.write( "0 2.5 8 26<BR>\n" );
document.write( "NR3=R3-2.5*R2<BR>\n" );
document.write( "1 -2.5 0 -11<BR>\n" );
document.write( "0 1 3 10<BR>\n" );
document.write( "0 0 0.5 1<BR>\n" );
document.write( "NR3=R3/0.5<BR>\n" );
document.write( "1 -2.5 0 -11<BR>\n" );
document.write( "0 1 3 10<BR>\n" );
document.write( "0 0 1 2<BR>\n" );
document.write( "NR2=R2-3R3<BR>\n" );
document.write( "1 -2.5 0 -11<BR>\n" );
document.write( "0 1 0 4<BR>\n" );
document.write( "0 0 1 2<BR>\n" );
document.write( "NR1=R1+2.5R2<BR>\n" );
document.write( "1 0 0 -1<BR>\n" );
document.write( "0 1 0 4<BR>\n" );
document.write( "0 0 1 2<BR>\n" );
document.write( "HENCE<BR>\n" );
document.write( "X=-1<BR>\n" );
document.write( "Y=4<BR>\n" );
document.write( "Z=2 </SPAN>\n" );
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