document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=986182>Question 986182</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which number is a root of f(x)=x^3+6x^2+9x that has multiplicity 1?\r<BR>\n" );
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document.write( " a. 3<BR>\n" );
document.write( " b. 1<BR>\n" );
document.write( " c. 0<BR>\n" );
document.write( " d. –3\r<BR>\n" );
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document.write( "Do you just substitute one of the numbers for x? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #606983 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=606983\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Replace f(x) with 0, then factor\r<BR>\n" );
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document.write( "f(x)=x^3+6x^2+9x<BR>\n" );
document.write( "0=x^3+6x^2+9x<BR>\n" );
document.write( "x^3+6x^2+9x = 0<BR>\n" );
document.write( "x(x^2+6x+9) = 0<BR>\n" );
document.write( "x(x+3)(x+3) = 0\r<BR>\n" );
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document.write( "Then use the zero product property to break up x(x+3)(x+3) = 0 into these three equations\r<BR>\n" );
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document.write( "x=0 or x+3=0 or x+3=0\r<BR>\n" );
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document.write( "The first equation x=0 means we have a root of 0. This root is of multiplicity 1\r<BR>\n" );
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document.write( "The other two equations are exact duplicates of one another. They both lead to x=-3 being the other root of multiplicity 2.\r<BR>\n" );
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document.write( "So in the end, the answer is <font color=\"red\">c. 0</font>\r<BR>\n" );
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document.write( "The graph confirms this. Notice how we have a double root at x = -3. It doesn't cross over the x axis as it only touches the x axis here. Contrast that with the root at x = 0 where it crosses through the x axis one time.\r<BR>\n" );
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