document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=968069>Question 968069</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The polynomial P(x)=x^4+ax^2+bx-9 has zeros at x=1 and x=-3. The values of a and b are... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #591652 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=591652\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the polynomial has zeroes at x = 1 and x = -3, then the value of the polynomial would have to be 0 when you replace x with either 1 or -3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you would get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(1) = 0 and f(-3) = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "start with your polynomial and set it to 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you will get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^4+ax^2+bx-9 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace x with 1 and the equation becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1^4 + a*1 + b*1 - 9 = 0<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "1 + a + b - 9 = 0<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "a + b - 8 = 0<BR>\n" );
document.write( "add 8 to both sides of the equation to get:<BR>\n" );
document.write( "a + b = 8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace x with -3 and the equation becomes:<BR>\n" );
document.write( "(-3)^4 + a*(-3)^2 + b*(-3) - 9 = 0<BR>\n" );
document.write( "simplify this to get:<BR>\n" );
document.write( "81 + 9a - 3b - 9 = 0<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "72 + 9a - 3b = 0<BR>\n" );
document.write( "subtract 72 from both sides of the equation to get:<BR>\n" );
document.write( "9a - 3b = -72\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have 2 equations that need to be solved simultaneously.<BR>\n" );
document.write( "they are:<BR>\n" );
document.write( "a + b = 8<BR>\n" );
document.write( "9a - 3b = -72\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "multiply both sides of the first equation by 9 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "9a + 9b = 72<BR>\n" );
document.write( "9a - 3b = -72\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract the second equation from the first to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "12b = 144\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for b to get b = 12\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "go back to the first equation and solve for a to get:<BR>\n" );
document.write( "a + b = 8 becomes:<BR>\n" );
document.write( "a + 12 = 8<BR>\n" );
document.write( "solve for a to get:<BR>\n" );
document.write( "a = 8 - 12 = -4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a = -4<BR>\n" );
document.write( "b = 12\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace those values in the original equation of x^4+ax^2+bx-9 = 0 to get:<BR>\n" );
document.write( "x^4 -4 * x^2 + 12 * x - 9 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you graph the equation using a graphing calculator that tells you the zero points, your graph will look like this:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/050401.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "another way would have been to evaluate the equation at f(1) and f(-3) when the value of a was -4 and the value of b was 12.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "f(1) and f(-3) should both have been equal to 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );