document.write( "Question 1077969: Let A and B be the roots of an equation x2 +ax+b=0 and let C and D be the roots of x2+cx+d=0. Express (A-C) (B-C) (A-D) (B-D) in terms of the coefficients a, b,c ,d. \n" ); document.write( "

Algebra.Com's Answer #692462 by ikleyn(52835) $\"\"$ $\"About$

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\n" ); document.write( "Let A and B be the roots of an equation x2 +ax+b=0 and let C and D be the roots of x2+cx+d=0.
\n" ); document.write( "Express (A-C) (B-C) (A-D) (B-D) in terms of the coefficients a, b,c ,d.
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document.write( "1.  (A-C)*(B-C) =  =  = .\r\n" );
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document.write( "    (I replaced here A+B by -a and replaced AB by b based on Vieta's formulas).\r\n" );
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document.write( "2.  (A-D)*(B-D) =  =  = .\r\n" );
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document.write( "    (Again, I replaced here A+B by -a and replaced AB by b based on Vieta's formulas).\r\n" );
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document.write( "3.  Now  (A-C)*(B-C)*(A-D)*(B-D) =  = \r\n" );
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document.write( "    =  = (regroup)\r\n" );
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document.write( "    =  = (simplify)\r\n" );
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document.write( "    =  = \r\n" );
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document.write( "      (replace D+C = -c,   =  = (-c)^2 -2d,  CD = d,  D+C = -c,  (CD)^2 = d^2  based on Vieta's formulas. You will get) \r\n" );
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document.write( "    =  = (simplify)\r\n" );
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document.write( "    =  = (I just got the expression via coefficients a, b, c and d !) = \r\n" );
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document.write( "    =  = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. (A-C)*(B-C)*(A-D)*(B-D) = $\"%28b-d%29%5E2+-ac%28b%2Bd%29+%2B+bc%5E2-a%5E2d\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Lesson to learn from this solution:\r
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document.write( "     This assignment is for those who firmly knows Vieta's formulas.\r\n" );
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