document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=755154>Question 755154</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The function f(x)=x^3-x+1 has exactly one real zero. It is between <BR>\n" );
document.write( "(A) -2 and -1<BR>\n" );
document.write( "(B) -1 and 0 <BR>\n" );
document.write( "(C) 0 and 1<BR>\n" );
document.write( "(D) 1 and 2 <BR>\n" );
document.write( "(E) 2 and 3 \r<BR>\n" );
document.write( "\n" );
document.write( "Can you please tell me how to get this answer? its on my final and i don't remember ever doing them...  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #459524 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=459524\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The function f(x)=x^3-x+1 has exactly one real zero. It is between <BR>\n" );
document.write( "(A) -2 and -1<BR>\n" );
document.write( "(B) -1 and 0 <BR>\n" );
document.write( "(C) 0 and 1<BR>\n" );
document.write( "(D) 1 and 2 <BR>\n" );
document.write( "(E) 2 and 3 <BR>\n" );
document.write( "Can you please tell me how to get this answer? its on my final and i don't remember ever doing them..<BR>\n" );
document.write( "***<BR>\n" );
document.write( "There is a rule I found called the Location Theorem which can be applied here.<BR>\n" );
document.write( "This is how it works: plug in consecutive x-values like a and b.<BR>\n" );
document.write( "If f(a) and f(b) have opposite signs, there is at least one real root between a and b.<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(A) a=-2, b=-1<BR>\n" );
document.write( "f(a)=f(-2)=-8+2+1=-5<BR>\n" );
document.write( "f(b)=f(-1)=-1+1+1=1<BR>\n" );
document.write( "f(a) and f(b) have opposite signs, so there is a real root between -2 and -1<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(B) a=-1, b=0<BR>\n" );
document.write( "f(a)=f(-1)=1<BR>\n" );
document.write( "f(b)=f(0)= 1<BR>\n" );
document.write( "f(a) and f(b) have same signs, so there isno real root between -1 and 0<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(C) a=0, b=1<BR>\n" );
document.write( "f(a)=f(0)=1<BR>\n" );
document.write( "f(b)=f(1)=1<BR>\n" );
document.write( "f(a) and f(b) have same signs, so there is no real roots between 0 and 1<BR>\n" );
document.write( "..<BR>\n" );
document.write( "You can try (D) and (E)  yourself.<BR>\n" );
document.write( "If you have a graphing calculator, you will find a real zero at -1.32472.., confirming that A is the ans. </SPAN>\n" );
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