document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209721>Question 1209721</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For parts (a)-(d), let p, q, r, and s be the roots of g(x) = 3x^4 - 8x^3 + 5x^2 + 2x - 17 - 2x^4 + 10x^3 + 11x^2 + 18x - 14.\r<BR>\n" );
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document.write( "Compute pqr + pqs + prs + qrs.<BR>\n" );
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document.write( "Answer: <font color=red>-20</font>\r<BR>\n" );
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document.write( "Explanation<BR>\n" );
document.write( "3x^4 - 8x^3 + 5x^2 + 2x - 17 - 2x^4 + 10x^3 + 11x^2 + 18x - 14<BR>\n" );
document.write( "simplifies to<BR>\n" );
document.write( "x^4 + 2x^3 + 16x^2 + 20x - 31\r<BR>\n" );
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document.write( "Consider the general quartic function<BR>\n" );
document.write( "f(x) = ax^4 + bx^3 + cx^2 + dx + e\r<BR>\n" );
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document.write( "According to <a  rel=nofollow HREF=\"https://mathworld.wolfram.com/VietasFormulas.html\">Vieta's formulas</a> (specifically formulas (4) and (5) on that page) we can state that,<BR>\n" );
document.write( "pqr + pqs + prs + qrs = -d/a = -20/1 = <font color=red>-20</font>\r<BR>\n" );
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document.write( "Another approach is to determine the approximate values of p,q,r,s<BR>\n" );
document.write( "p = -2.1259 <BR>\n" );
document.write( "q = 0.8627<BR>\n" );
document.write( "r = -0.3684 + 4.0948i<BR>\n" );
document.write( "s = -0.3684 - 4.0948i<BR>\n" );
document.write( "The order of the roots doesn't matter.<BR>\n" );
document.write( "Then use a calculator to get this approximate result<BR>\n" );
document.write( "pqr + pqs + prs + qrs = -20.0007015303<BR>\n" );
document.write( "If you were to use more decimal digits in each of the four roots, then you would get closer to <font color=red>-20</font><BR>\n" );
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