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If (x + J) (x + k) is equivalent to x2 + 9x - 20 for all values of x, what is j+ K?

User Frederic
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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.

User Pritesh
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