Answer:
To solve this problem, we can use FOIL to expand the left-hand side of the equation:
(x + j) (x + k) = x^2 + kx + jx + jk
We know that this is equivalent to x^2 + 9x - 20 for all values of x. Therefore, we can set the coefficients of the expanded equation equal to the coefficients of the given equation:
k + j = 9
jk = -20
We need to find the value of j + k. We can solve for k and substitute it into the first equation:
k = 9 - j
j(9 - j) = -20
9j - j^2 = -20
j^2 - 9j - 20 = 0
(j - 5)(j - 4) = 0
Therefore, j = 5 or j = 4. If j = 5, then k = 4. If j = 4, then k = 5. In either case, j + k = 9. Therefore, j + k = 9.