The solutions to the equation 2x2+x-1=2 are x=-3/2 or x=_

the solutions are {1, -3/2}

Step-by-step 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}.

3

step-by-step explanation: