Question 1147780
<br>
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<br>
{{{ax^4+bx^3+10x^2-18x+9}}}<br>
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.<br><pre>

   1  |  a     b     10     -18     9
      |
      |        a    a+b   a+b+10  a+b-8
      +---------------------------------
         a    a+b  a+b+10 a+b-8   a+b+1<br></pre>
Since 1 is a root, {{{a+b+1 = 0}}}, which means {{{a+b = -1}}}<br>
ANSWER: a+b = -1