Find all the values of a for which the equations

x^2 + ax + 1 = 0

x^2 - 3x - a = 0

have a common real root. Enter all the possible values, separated by commas.

in order for the first one to be real, you would need

(x+1)(x+1) where a is 2

or (x-1)(x-1) where a is -2

putting in 2 for a in the second equation is not a real root

putting -2 for a in the second equation gives us

(x-2)(x-1)

this if a=-2 then x=1 is the common root