document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186256>Question 1186256</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the quadratic formula to solve 2x^8 - 7x^4 - 3 = 0. Write your answer correct to 3 significant figures. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #817142 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=817142\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is 2x^8 - 7x^4 - 3 = 0.\r<BR>\n" );
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document.write( "this is equivalent to:\r<BR>\n" );
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document.write( "2 * (x^4) ^ 2 - 7 * (x^4) ^ 1 - 3 = 0\r<BR>\n" );
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document.write( "if you replace x^4 with y, the equation becomes:\r<BR>\n" );
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document.write( "2y^2 - 7y - 3 = 0\r<BR>\n" );
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document.write( "this in standard form of ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "when you replace x with y, it becomes:\r<BR>\n" );
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document.write( "ay^2 + by + c = 0\r<BR>\n" );
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document.write( "if you solve the quadratic equation using the quadratic formula, you will get:\r<BR>\n" );
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document.write( "y = 3.886000936 or y = -0.386000936\r<BR>\n" );
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document.write( "since y = x^4, solve this for x to get:\r<BR>\n" );
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document.write( "x = (3.886000936) ^ (1/4) or y = (-0.386000936) ^ (1/4).\r<BR>\n" );
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document.write( "you will find that the first option will get you x = plus or minus 1.404027859.\r<BR>\n" );
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document.write( "you will find that the second option will get you x = undefined because you can't take the even root of a negative number and get a real number as an answer.\r<BR>\n" );
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document.write( "you can get a complex number as an answer, but not a real number.\r<BR>\n" );
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document.write( "your solution becomes:\r<BR>\n" );
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document.write( "x = plus or minus fourth root of 3.886000936 which is equal to plus or minus 1.404027859.\r<BR>\n" );
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document.write( "if you graph the equation of y = 2x^8 - 7x^4 - 3, you will find that the roots are plus or minus 1.404 when rounded to 3 decimal places, as shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2021/101711.jpg\" >\r<BR>\n" );
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document.write( "here is the quadratic formula.\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" );
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document.write( "               (-b plus or minus sqrt(b^2 - 4ac)\r\n" );
document.write( "x =          --------------------------------------\r\n" );
document.write( "                              2a\r\n" );
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document.write( "</PRE>                 \r<BR>\n" );
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document.write( " </SPAN>\n" );
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