document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=58903>Question 58903</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321279085/algebrahomeworkh>College Algebra with Modeling and Visualization</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Complete the following:<BR>\n" );
document.write( "a)  Find all zeros of f(x).<BR>\n" );
document.write( "b)  Write the complete factored form of f(x).\r<BR>\n" );
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document.write( "f(x) = x^4 + 5x^2 + 4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #40403 by </B><A HREF=/tutors/aboutme.mpl?userid=uma><B>uma(370)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=uma><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=40403\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = x^4 + 5x^2 + 4<BR>\n" );
document.write( "Let x^4 + 5x^2 + 4 = 0..............(1)<BR>\n" );
document.write( "Let x^2 = y, then x^ 4 = y^2<BR>\n" );
document.write( "So eqn (1) becomes y^2 + 5y + 4 = 0<BR>\n" );
document.write( "           ==>     y^2 + y + 4y + 4 = 0 [Splitting the middle term]<BR>\n" );
document.write( "           ==>     y(y+1) + 4(y+1) = 0<BR>\n" );
document.write( "           ==>     (y+1) (y+4) = 0<BR>\n" );
document.write( "           ==>     y+1 = 0   or  y+4 = 0<BR>\n" );
document.write( "           ==>     y = -1 [adding -1 to both the sides] or y = -4 [Adding -4]<BR>\n" );
document.write( "           ==>     x^2 = -1  or x^2 = -4 [because y = x^2]<BR>\n" );
document.write( "           ==>     x = sqrt(-1)  or x = sqrt(-4)  [taking sqrt]<BR>\n" );
document.write( "We know that sqrt(-1) = i<BR>\n" );
document.write( "Therefore sqrt(-1) = i 0r -i and sqrt(-4) = 2i or -2i\r<BR>\n" );
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document.write( "Thus the zeroes of the given function are i, -i, 2i and -2i\r<BR>\n" );
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document.write( "f(x) = x^4 + 5x^2 + 4<BR>\n" );
document.write( "     = (x+i)(x-i)(x+2i)(x-2i)\r<BR>\n" );
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document.write( "Regards,<BR>\n" );
document.write( "Uma\r<BR>\n" );
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document.write( " </SPAN>\n" );
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