Answer:
c = 49/4
Explanation:
The given expression is x^2 - 7x + c
This trinomial must be a perfect square.
Therefore, c must be a prefect square number.
So b^2 - 4ac = 0. That is discriminant must be equal to zero.
In the given expression a =1 and b = -7
Now plug in these values in the discriminant formula.
(-7)^2 - 4*1*c = 0
49 -4c = 0
4c = 49
c = 49/4
x^2 - 7x + 49/4 = (x - 7/2)^2
which is perfect square trinomial.
Thank you.