Answer:
If c>0, then the solution is imaginary, which is not a real solution.
Explanation:
ax^2 + c = 0, with a > 0
Subtract c from each side
ax^2 +c-c = 0-c
ax^2 = -c
Divide each side by a
ax^2/a = -c/a
x^2 = -c/a
Take the square root of each side
sqrt(x^2) = sqrt(-c/a)
AAAAAAAH
The only way to have real square roots is for -c/a to be positive.
We know that a>0, so -c >0
-c>0
Divide each side by -1, remembering to flip the inequality
c<0
If c<0 we have real solutions
If c=0 then x=0 which is a real solution
If c>0, then the solution is imaginary, which is not a real solution.