Answer:
c > 1
Explanation:
For a quadratic equation of the form ax^2 + bx + c = 0 to have no real roots, its discriminant (b^2 - 4ac) must be negative.
In the given quadratic equation, a = 1, b = -2, and c = c. So the discriminant is:
b^2 - 4ac = (-2)^2 - 4(1)(c) = 4 - 4c
For the equation to have no real roots, we need:
b^2 - 4ac < 0
4 - 4c < 0
Solving for c, we get:
4c > 4
c > 1
Therefore, for c > 1, the quadratic equation x^2 - 2x + c = 0 has no real roots.