To find the discriminant of the quadratic equation \(5x^2 - 10x + 5 = 0\), we can use the formula for the discriminant, which is given by:
\[ D = b^2 - 4ac \]
where \(a\), \(b\), and \(c\) are the coefficients of the quadratic equation \(ax^2 + bx + c = 0\).
Here, we have:
- \(a = 5\)
- \(b = -10\)
- \(c = 5\)
Now we can compute the discriminant:
\[ D = (-10)^2 - 4(5)(5) \] \[ D = 100 - 100 \] \[ D = 0 \]
The discriminant \(D = 0\) indicates that the quadratic equation has exactly one real solution.
To summarize:
- The discriminant of the quadratic equation is \(0\).
- The number of real solutions is \(1\).
So the correct answer is: 2) one real solution.