document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042946>Question 1042946</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.\r<BR>\n" );
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document.write( "f(x) = 8x3 - 10x2 + 3x + 5; [-1, 0]\r<BR>\n" );
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document.write( "    a. no real roots; f(x) = (x2 + 1)(3x2 + 1)<BR>\n" );
document.write( "    b. 1, multiplicity 2; f(x) = (x - 1)2(3x2 + 1)<BR>\n" );
document.write( "    c. -1, 1; f(x) = (x - 1)(x + 1)(3x2 + 1)<BR>\n" );
document.write( "    d. -1, multiplicity 2; f(x) = (x + 1)2(3x2 + 1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #658034 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=658034\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( " Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval.\r<BR>\n" );
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document.write( "f(x) = 8x^3 - 10x^2 + 3x + 5; [-1, 0]\r<BR>\n" );
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document.write( "    a. no real roots; f(x) = (x2 + 1)(3x2 + 1)<BR>\n" );
document.write( "    b. 1, multiplicity 2; f(x) = (x - 1)2(3x2 + 1)<BR>\n" );
document.write( "    c. -1, 1; f(x) = (x - 1)(x + 1)(3x2 + 1)<BR>\n" );
document.write( "    d. -1, multiplicity 2; f(x) = (x + 1)2(3x2 + 1)<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
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document.write( "They ask you to apply <U>the intermediate value theorem</U>.\r<BR>\n" );
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document.write( "Do you know what \"the intermediate value theorem\" is?\r<BR>\n" );
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document.write( "I specially copied and pasted this citation for you from this Wikipedia <A  rel=nofollow HREF=https://en.wikipedia.org/wiki/Intermediate_value_theorem>article</A>.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "    In mathematical analysis, the intermediate value theorem states that if a continuous function, f, with an interval, [a, b], \r\n" );
document.write( "    as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) \r\n" );
document.write( "    at some point within the interval.\r\n" );
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document.write( "    This has an important corollary: If a continuous function has values of opposite sign inside an interval, then it has a root\r\n" );
document.write( "    in that interval (Bolzano's theorem).\r\n" );
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document.write( "It seems strange to me what follows after the assignment.\r<BR>\n" );
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document.write( "In n.n. a, b, c, and d I see the listing of the roots and factoring formulas,\r<BR>\n" );
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document.write( "and I do not understand how it correlates with the assignment.\r<BR>\n" );
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document.write( "Let me say more.<BR>\n" );
document.write( "No one factorization a), b), c), d) corresponds to the given polynomial.\r<BR>\n" );
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document.write( "My impression is that somebody, who understands NOTHING in these topics, mistakenly merged different parts of different assignments in one post.<BR>\n" );
document.write( "And then sent it trice !!!\r<BR>\n" );
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document.write( "<U>DIAGNOSIS</U>. This post is one big fatal error and does not deserve any serious consideration.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The sender must ask pardon for sending this post. <BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Ask the pardon three times, according to the number of issued copies of this post.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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