document.write( "Question 1129676: If F(x)=ax^2 +bx+c and F(x+5)=x^2+9x-7, find the sum of a+b+c. \n" ); document.write( "

Algebra.Com's Answer #746322 by ikleyn(52782) $\"\"$ $\"About$

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document.write( "You have two sources of information:\r\n" );
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document.write( "    1)  F(x) = ax^2 + bx + c   (a general definition of the polynomial F(x)).\r\n" );
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document.write( "        From it,  a + b + c = F(1).\r\n" );
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document.write( "    2)  You also are given the second piece of information:  F(x+5) = x^2 + 9x - 7.\r\n" );
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document.write( "        To get F(1), you need to take x = -4 in the last identity, and then you will get\r\n" );
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document.write( "        a + b + c = F(1) = F(-4 + 5) = (-4)^2 + 9*(-4) - 7 = 16 - 36 - 7 = -27.\r\n" );
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document.write( "ANSWER.  a + b + c = -27.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "This problem is good for an interview, if the company wants to hire someone with creative mathematical mind.\r
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\n" ); document.write( "\n" ); document.write( "If the interviewed person solves it in this way, he (or she) deserves the \" + \" sign in the answer list.\r
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\n" ); document.write( "\n" ); document.write( "If he (or she) will solve it by another way (by direct substituting and manipulating coefficients), he (or she) deserves \" - \"
\n" ); document.write( "(even if he (or she) will get a correct answer finally).\r
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\n" ); document.write( "\n" ); document.write( "Typical \"Math circle\" level problem.\r
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