document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1046439>Question 1046439</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the zeros of a given function f are -1,2, and 5. <BR>\n" );
document.write( "a. What are the zeros of the function g(x)=2f(x)?\r<BR>\n" );
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document.write( "b. What are the zeros of the function h(x)=f(2x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #661885 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=661885\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "the zeros of a given function f are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=+-1 ALIGN=MIDDLE  ALT=\"x%5B1%5D=+-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%5B2%5D=2 ALIGN=MIDDLE  ALT=\"x%5B2%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D=5 ALIGN=MIDDLE  ALT=\"x%5B3%5D=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "use zero product theorem to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x-%28-1%29%29%28x-2%29%28x-5%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x-%28-1%29%29%28x-2%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%2B1%29%28x-2%29%28x-5%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B1%29%28x-2%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%2B1%29%28x-2%29%28x-5%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B1%29%28x-2%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3-6x%5E2%2B3x%2B10 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3-6x%5E2%2B3x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a. What are the zeros of the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=2f%28x%29 ALIGN=MIDDLE  ALT=\"g%28x%29=2f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >?\r<BR>\n" );
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document.write( "use factored form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=%28x%2B1%29%28x-2%29%28x-5%29 ALIGN=MIDDLE  ALT=\"f%28x%29=%28x%2B1%29%28x-2%29%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29=2%28%28x%2B1%29%28x-2%29%28x-5%29%29 ALIGN=MIDDLE  ALT=\"g%28x%29=2%28%28x%2B1%29%28x-2%29%28x-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+2+%28x-5%29+%28x-2%29+%28x%2B1%29 ALIGN=MIDDLE  ALT=\"0+=+2+%28x-5%29+%28x-2%29+%28x%2B1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >...basically nothing will change<BR>\n" );
document.write( "the zeros of a  function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%28x%29 ALIGN=MIDDLE  ALT=\"g%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are same as of a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+f%28x%29 ALIGN=MIDDLE  ALT=\"+f%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=+-1 ALIGN=MIDDLE  ALT=\"x%5B1%5D=+-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%5B2%5D=2 ALIGN=MIDDLE  ALT=\"x%5B2%5D=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D=5 ALIGN=MIDDLE  ALT=\"x%5B3%5D=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b. What are the zeros of the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29=f%282x%29+ ALIGN=MIDDLE  ALT=\"h%28x%29=f%282x%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=x%5E3-6x%5E2%2B3x%2B10 ALIGN=MIDDLE  ALT=\"f%28x%29=x%5E3-6x%5E2%2B3x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29=f%282x%29+=%282x%29%5E3-6+%282x%29%5E2%2B3+%282x%29%2B10 ALIGN=MIDDLE  ALT=\"h%28x%29=f%282x%29+=%282x%29%5E3-6+%282x%29%5E2%2B3+%282x%29%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29+=8x%5E3-24x%5E2%2B6x%2B10 ALIGN=MIDDLE  ALT=\"h%28x%29+=8x%5E3-24x%5E2%2B6x%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29++=+2%282x%2B1%29%282x-5%29%28x-1%29 ALIGN=MIDDLE  ALT=\"h%28x%29++=+2%282x%2B1%29%282x-5%29%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%282x%2B1%29+%282+x-5%29+%28x-1%29=0 ALIGN=MIDDLE  ALT=\"2%282x%2B1%29+%282+x-5%29+%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+%282x%2B1%29+=0 ALIGN=MIDDLE  ALT=\"2+%282x%2B1%29+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B1%29+=0 ALIGN=MIDDLE  ALT=\"%282x%2B1%29+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=-1%2F2 ALIGN=MIDDLE  ALT=\"x+=-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282+x-5%29+=0%7B%7B%7B-%3E+then+%7B%7B%7B2x=5 ALIGN=MIDDLE  ALT=\"%282+x-5%29+=0%7B%7B%7B-%3E+then+%7B%7B%7B2x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5%2F2 ALIGN=MIDDLE  ALT=\"x=5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29=0 ALIGN=MIDDLE  ALT=\"%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );