Final answer:
The quadratic equation x² - 10x + 25 = 0 has one real root. Since the discriminant is zero, the equation has only one real root, which is repeated. In this case, the root is x = 5.
Step-by-step explanation:
To find the discriminant and determine the number and type of roots for the equation x² - 10x + 25 = 0, we can use the quadratic formula.
The quadratic formula is given by x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
For the given equation, a = 1, b = -10, and c = 25.
Substituting these values into the quadratic formula, we get x = (-(-10) ± √((-10)² - 4(1)(25))) / (2(1)).
Simplifying further, x = (10 ± √(100 - 100)) / 2.
The discriminant is the value inside the square root, which in this case is 0.
Since the discriminant is zero, the equation has only one real root, which is repeated. In this case, the root is x = 5.