Find the value of a for which the function has repeated factors.
If is the repeated root, is the factor ___(1) ___(2)
This is as far as I got.
That is a good way to start the problem. To continue, divide your equation (2) by 2, then multiply it by and subtract the resulting equation from equation (1). That will get rid of the terms containing , leaving you with a cubic equation for (for which you ought to be able to spot one of the roots).