Answer:
the solutions are {1, -3/2}
Explanation:
The given equation 2x^2 + x - 1 = 2 simplifies to 2x^2 + x - 3 = 0 if we subtract 2 from both sides.
We are told that -3/2 is a solution and must find the other solution To do this, use synthetic division; if the remainder is zero, that tells us that -3/2 is actually a solution, and we can obtain the second solution easily, as follows:
-3/2 / 2 1 -3
-3 3
-------------------------
2 -2 0
Since the remainder is 0, we have verified that -3/2 is a solution. The coefficients of the other factor of the original equation are 2 and -2, and so this other factor is 2x - 2, or 2(x - 1). Setting this result equal to zero yields x = 1.
Thus the solutions are {1, -3/2}.