document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1126946>Question 1126946</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a polynomial of the specified degree that satisfies the given conditions. <BR>\n" );
document.write( "Degree 5;    zeros &#8722;3, &#8722;1, 3 and \r<BR>\n" );
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document.write( "square of 3<BR>\n" );
document.write( ";    integer coefficients and constant term 54 </SPAN>\n" );
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document.write( "In order for the problem to make sense, I will assume that the last root you show is the square ROOT of 3, not the square of 3.<br><BR>\n" );
document.write( "Then, since the polynomial is to have integer coefficients, the 5th root must be negative square root of 3.<br><BR>\n" );
document.write( "The polynomial with those 5 roots is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%28x%2B3%29%28x%2B1%29%28x-3%29%28x-sqrt%283%29%29%28x%2Bsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"a%28x%2B3%29%28x%2B1%29%28x-3%29%28x-sqrt%283%29%29%28x%2Bsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The constant term of the polynomial is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%283%29%281%29%28-3%29%28-3%29+=+27a ALIGN=MIDDLE  ALT=\"a%283%29%281%29%28-3%29%28-3%29+=+27a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Since the constant term is 54, a must be 2.  Then the polynomial (still in factored form) is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B3%29%28x%2B1%29%28x-3%29%28x-sqrt%283%29%29%28x%2Bsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"2%28x%2B3%29%28x%2B1%29%28x-3%29%28x-sqrt%283%29%29%28x%2Bsqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In expanded form the polynomial is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%5E2-9%29%28x%5E2-3%29%28x%2B1%29+=+2%28x%5E4-12x%5E2%2B27%29%28x%2B1%29+=+2%28x%5E5%2Bx%5E4-12x%5E3-12x%5E2%2B27x%2B27%29+=+2x%5E5%2B2x%5E4-24x%5E3-24x%5E2%2B54x%2B54 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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