document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192454>Question 1192454</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the intermediate value theorem to show that the function has a zero between the two numbers given.​ Then, use your calculator to approximate the zero to the nearest hundredth.<BR>\n" );
document.write( "P(x)=6x^4-6x^2+4x-2;0.5 and 1<BR>\n" );
document.write( "Any help is appreciated thank you! </SPAN>\n" );
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document.write( "Plug in x = 0.5<BR>\n" );
document.write( "P(x)=6x^4-6x^2+4x-2<BR>\n" );
document.write( "P(0.5)=6(0.5)^4-6(0.5)^2+4(0.5)-2<BR>\n" );
document.write( "P(0.5)=-1.125<BR>\n" );
document.write( "The result is negative.\r<BR>\n" );
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document.write( "Repeat for x = 1<BR>\n" );
document.write( "P(x)=6x^4-6x^2+4x-2<BR>\n" );
document.write( "P(1)=6(1)^4-6(1)^2+4(1)-2<BR>\n" );
document.write( "P(1)=2<BR>\n" );
document.write( "The result is positive.\r<BR>\n" );
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document.write( "The actual numeric values don't matter. <BR>\n" );
document.write( "All we care about are the signs of the results.\r<BR>\n" );
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document.write( "The value of P(0.5) is negative and P(1) is positive.\r<BR>\n" );
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document.write( "The transition from negative to positive means that somewhere along the line is at least one x intercept or root. <BR>\n" );
document.write( "This is because the curve is continuous meaning there aren't any gaps or jumps.<BR>\n" );
document.write( "Any polynomial is continuous.\r<BR>\n" );
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document.write( "Using a graphing calculator like desmos or geogebra would show that the root on this interval is roughly x = 0.83<BR>\n" );
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