# #m# is a real number. #(x^2-mx+8) . (x-1) = 0# has two distinct roots. What are all #m# values?

##### 1 Answer

There are three possible

#### Explanation:

(This answer operates under the assumption that there are *exactly* two distinct roots, rather than *at least* two distinct roots)

or

If the first is true, then

Equating corresponding coefficients, we have

Thus, from the first equation, we have two possibilities for

If the second equation is true, then

Again, we equate corresponding coefficients to obtain

Therefore, from the second equation, we have one possibility for

So, putting them together, there are three possible