The equation x^2 + (k-5)x + 1 = 0 has equal roots. Determine the possible values of k.

So the first part of this question is regarding your knowledge and understanding on the subject matter. You should know that for real and equal roots, (b² - 4ac)=0. (For real and unequal roots, it is >0 and for non-real roots, it is <0.)
Once we know this, we can find the values of a, b and c using the equation. Where a =1, b=(k-5) and c=1.Next, we need to solve for (b² - 4ac)=0.
(k-5)²- (411) = 0 (k-5)²- 4 = 0
The next step is to expand the brackets:
k² - 10k +25 - 4 = 0k² - 10k +21 = 0
Finally, we are left with an equation which can be factored to find the values of k, as follows:
(k-7) (k-3) = 0
Therefore, k = 7 or k =3.