document.write( "Question 1147780: “A quartic function in the form f(x) = ax^4 + bx^3 + cx^2 + dx + e is such that the coefficient of the quadratic and linear terms are 10 and -18 respectively. Additionally, f(0) =9 and x=1 is a root with a multiplicity of two. What is the value of (a +b)? \n" ); document.write( "

Algebra.Com's Answer #769130 by greenestamps(13198) $\"\"$ $\"About$

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\n" ); document.write( "The values of c and d are given in the statement of the problem; and f(0)=9 tells us e is 9. So the function is

\n" ); document.write( " $\"ax%5E4%2Bbx%5E3%2B10x%5E2-18x%2B9\"$

\n" ); document.write( "Synthetic division knowing that x=1 is a root then gives us the answer to the question that is asked. The fact that x=1 is a root of multiplicity 2 is not needed.

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document.write( "\r\n" );
document.write( "   1  |  a     b     10     -18     9\r\n" );
document.write( "      |\r\n" );
document.write( "      |        a    a+b   a+b+10  a+b-8\r\n" );
document.write( "      +---------------------------------\r\n" );
document.write( "         a    a+b  a+b+10 a+b-8   a+b+1

\n" ); document.write( "Since 1 is a root, $\"a%2Bb%2B1+=+0\"$ , which means $\"a%2Bb+=+-1\"$

\n" ); document.write( "ANSWER: a+b = -1 \n" ); document.write( "

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