document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172151>Question 1172151</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.If r and s are the roots of the quadratic equation x2 + 3x  -  5 = 0, find the value of r3 + s3. Show clear solution pls thanksss! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #797067 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=797067\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "We can use Vieta's Formulas to say<BR>\n" );
document.write( "r+s = -b<BR>\n" );
document.write( "r*s = c<BR>\n" );
document.write( "where r,s are the two roots of x^2+bx+c<BR>\n" );
document.write( "In this case, a = 1.<BR>\n" );
document.write( "If 'a' was some nonzero value other than 1, then you'd have to divide everything by 'a' to get ax^2+bx+c into the form x^2+px+q, where p = b/a and q = c/a.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "From x^2+3x-5, we see that b = 3 and c = -5<BR>\n" );
document.write( "Plug those values into the first two equations mentioned to get:<BR>\n" );
document.write( "r+s = -3<BR>\n" );
document.write( "r*s = -5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's square both sides of that first equation and do a bit of rearranging:<BR>\n" );
document.write( "r+s = -3<BR>\n" );
document.write( "(r+s)^2 = (-3)^2<BR>\n" );
document.write( "r^2+2rs+s^2 = 9<BR>\n" );
document.write( "r^2+s^2+2rs = 9<BR>\n" );
document.write( "r^2+s^2+2(-5) = 9 ... plug in rs = -5<BR>\n" );
document.write( "r^2+s^2-10 = 9<BR>\n" );
document.write( "r^2+s^2 = 9+10<BR>\n" );
document.write( "r^2+s^2 = 19\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The following three equations<BR>\n" );
document.write( "r+s = -3<BR>\n" );
document.write( "r*s = -5<BR>\n" );
document.write( "r^2+s^2 = 19<BR>\n" );
document.write( "will be used in the next portion below\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "By the sum of cubes factoring formula, we know that...<BR>\n" );
document.write( "r^3+s^3 = (r+s)(r^2-rs+s^2)<BR>\n" );
document.write( "r^3+s^3 = (r+s)(r^2+s^2-rs)<BR>\n" );
document.write( "r^3+s^3 = (-3)(r^2+s^2-rs) ... plug in r+s = -3<BR>\n" );
document.write( "r^3+s^3 = (-3)(19-rs) .... plug in r^2+s^2 = 19<BR>\n" );
document.write( "r^3+s^3 = (-3)(19-(-5)) .... plug in rs = -5<BR>\n" );
document.write( "r^3+s^3 = (-3)(19+5)<BR>\n" );
document.write( "r^3+s^3 = (-3)(24)<BR>\n" );
document.write( "r^3+s^3 = <font color=red>-72</font> which is the final answer.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "As you can see from the last section, we computed r^3+s^3 without knowing what r and s are individually. We could actually solve for them using the quadratic formula\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I won't show those steps, but you should get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3%2Bsqrt%2829%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28-3%2Bsqrt%2829%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3-sqrt%2829%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28-3-sqrt%2829%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > as the two roots. <BR>\n" );
document.write( "These are the values of r and s in either order.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Once you know these values, plug them into r^3+s^3 and you should get -72 as the final answer. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also, knowing the actual roots r,s allows you to check each of these following equations<BR>\n" );
document.write( "r+s = -3<BR>\n" );
document.write( "r*s = -5<BR>\n" );
document.write( "r^2+s^2 = 19<BR>\n" );
document.write( "to help further confirm the steps of the previous section. I'll let you perform these checks.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: <font color=red>-72</font><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );