document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117426>Question 117426</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.)  What is a polynomial function in standard form of degree 4 with zeros: -1, 2, 5i?\r<BR>\n" );
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document.write( "2.)  Given f(x)=5x+1<BR>\n" );
document.write( "     Find f^-1(x) & verify the answer is correct by showing that (fof^-1)(x)=x\r<BR>\n" );
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document.write( "3.)  solve: a) log (x+4) - log 2x=0<BR>\n" );
document.write( "b) 2ln x + 5 = 7\r<BR>\n" );
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document.write( "4.)  Find all the zeros of the polynomial function:  P(x)=2x^4+3x^3+16x^2+27x-18 then write the P(x) as a product of its linear factors.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85432 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=85432\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.)  For any polynomial equation with real coefficients, complex roots occur in conjugate pairs.<BR>\n" );
document.write( "So, if 5i i.e. (0 + 5i) is a root then (0 - 5i) is the other root.<BR>\n" );
document.write( "Hence, the 4 zeros are x = -1, 2, 5i, - 5i<BR>\n" );
document.write( "Hence the polynomial is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+%28-1%29%29%28x+-+2%29%28x+-+5i%29%28x+-+%28-5i%29%29 ALIGN=MIDDLE  ALT=\"%28x+-+%28-1%29%29%28x+-+2%29%28x+-+5i%29%28x+-+%28-5i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+1%29%28x+-+2%29%28x+-+5i%29%28x+%2B5i%29 ALIGN=MIDDLE  ALT=\"%28x+%2B+1%29%28x+-+2%29%28x+-+5i%29%28x+%2B5i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+1%29%28x+-+2%29%28x%5E2+-+25i%5E2%29 ALIGN=MIDDLE  ALT=\"%28x+%2B+1%29%28x+-+2%29%28x%5E2+-+25i%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+1%29%28x+-+2%29%28x%5E2+%2B+25%29 ALIGN=MIDDLE  ALT=\"%28x+%2B+1%29%28x+-+2%29%28x%5E2+%2B+25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+x+-+2%29%28x%5E2+%2B+25%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+x+-+2%29%28x%5E2+%2B+25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4+-+x%5E3+%2B+23x%5E2+-+25x+-+50 ALIGN=MIDDLE  ALT=\"x%5E4+-+x%5E3+%2B+23x%5E2+-+25x+-+50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2.)  <BR>\n" );
document.write( "f(x) = 5x + 1<BR>\n" );
document.write( "5x = f(x) - 1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28f%28x%29-1%29%2F5 ALIGN=MIDDLE  ALT=\"x+=+%28f%28x%29-1%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hence, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%5E%28-1%29%28x%29+=+%28x+-+1%29%2F5 ALIGN=MIDDLE  ALT=\"f%5E%28-1%29%28x%29+=+%28x+-+1%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Verification:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28f%5E%28-1%29%28x%29%29+=+5f%5E%28-1%29%28x%29+%2B+1+=+5%28x-1%29%2F5+%2B+1+=+x ALIGN=MIDDLE  ALT=\"f%28f%5E%28-1%29%28x%29%29+=+5f%5E%28-1%29%28x%29+%2B+1+=+5%28x-1%29%2F5+%2B+1+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3.a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2Cx%2B4%29+-+log+%2810%2C2x%29+=+0 ALIGN=MIDDLE  ALT=\"log%2810%2Cx%2B4%29+-+log+%2810%2C2x%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%2810%2C%28x%2B4%29%2F2x%29+=+0 ALIGN=MIDDLE  ALT=\"log%2810%2C%28x%2B4%29%2F2x%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%2F2x+=+1 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%2F2x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29+=+2x ALIGN=MIDDLE  ALT=\"%28x%2B4%29+=+2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4 ALIGN=MIDDLE  ALT=\"x+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "3.b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2log%28e%2Cx%29+%2B+5+=+7 ALIGN=MIDDLE  ALT=\"2log%28e%2Cx%29+%2B+5+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2log%28e%2Cx%29+=+7+-+5+=+2 ALIGN=MIDDLE  ALT=\"2log%28e%2Cx%29+=+7+-+5+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%28e%2Cx%29+=+1 ALIGN=MIDDLE  ALT=\"log%28e%2Cx%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+e ALIGN=MIDDLE  ALT=\"x+=+e\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "4.) Try yourself! </SPAN>\n" );
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