Answer:
The "other" or "second" root is 4.
Step-by-step explanation:
We are told that -2.5 is a root of the equation. The coefficient b of the x term is unknown, and must be determined. Because -2.5 is a root, synthetic division with -2.5 as divisor must return a remainder of zero.
Setting up synthetic division, we arrive at:
-2.5 / 2 -b -20
-5 +12.5 + 2.5b
-------------------------------------
2 -5-b -7.5 + 2.5b
The remainer, -7.5 + 2.5b, must be zero (0). Thus, 2.5b = 7.5, and b = 3.
Then the other factor has the coefficients {2, -5-b}, and because b = 3, this comes out to coefficients {2, -8}.
The other factor is 2x - 8, which, if set equal to 0, yields x = 4. This is the "other root."
