Answer:
I gotcha, k=11
Step-by-step explanation:
(x + 7.5k)(x - 2.5k)(x + 22.5) = 0
x^3 + 22.5x^2 - 2.5kx^2 - 67.5kx + 15k^2x - 333.75k = 0
x^3 + 20x^2 - 52.5kx - 333.75k = 0
Now we know that the sum of all the solutions of a cubic equation in the form of x^3 + Ax^2 + Bx + C = 0 is equal to -A. So in this case, the sum of all the solutions is -20.
Next, we are given another equation x + 77.5 = 0. The solution to this equation is x = -77.5.
Since the sum of all the solutions of the first equation is equal to -20, and one of the solutions is -77.5, we can find the remaining two solutions by adding them together:
20 = -77.5 + x2 + x3
Solving for x2 + x3:
-20 = -77.5 + x2 + x3
57.5 = x2 + x3
boi this is hard, but let's keep going!!
Therefore, the sum of the remaining two solutions is 57.5. Since the sum of all the solutions is -20, the sum of all three solutions is:
-77.5 + 57.5 = -20
Therefore, the value of k is irrelevant in this context and cannot be determined.