document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=523322>Question 523322</A>: <I><SPAN STYLE=\"word-break: break-all;\"> suppose the roots of ax^2 + bx + c =0 are r and s. which one of the following has roots ar + b and as + b ? \r<BR>\n" );
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document.write( "(A)  x^2 - bx - ac =0\r<BR>\n" );
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document.write( "(B)  x^2 - bx + ac =0\r<BR>\n" );
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document.write( "(C) x^2 + 3bx + ca + 2b^2 =0\r<BR>\n" );
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document.write( "(D) x^2 + 3bx - ca + 2b^2 =0\r<BR>\n" );
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document.write( "(E) not given \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #347388 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=347388\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Recall that, if z is a root of a polynomial, then x-z is a factor of the polynomial.\r<BR>\n" );
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document.write( "Hence, we can write our new polynomial equation as (x - (ar + b))(x - (as + b)) = 0. Expanding the LHS, this yields\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^2 - x(as + b) - x(ar + b) + (ar + b)(as + b) = 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \Rightarrow x^2 - x(2b + ar + as) + (a^2rs + ab(r+s) + b^2) = 0\">\r<BR>\n" );
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document.write( "Recall that by Vieta's formulas, r+s = -b/a and rs = c/a. We can substitute these expressions in:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \Rightarrow x^2 - x(2b + a(-\frac{b}{a})) + (a^2(\frac{c}{a}) + ab(-\frac{b}{a}) + b^2) = 0\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \Rightarrow x^2 - bx + (ac - b^2 + b^2) = 0\">\r<BR>\n" );
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document.write( "b^2 cancels, so you will see that this equation is the same as in answer choice B. </SPAN>\n" );
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