Given:
The equation is x^2 - 3x + k = 0.
One of the roots is 2.

To find:
The value of k.

Solution:

1. Understanding the Problem:
The given equation is a quadratic equation. A quadratic equation is of the form ax^2 + bx + c = 0, where a, b, and c are constants. Here, we are given that one of the roots is 2. We need to find the value of k.

2. Understanding the Roots of a Quadratic Equation:
In a quadratic equation ax^2 + bx + c = 0, the roots can be found using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)

If a quadratic equation has real and distinct roots, then the discriminant (b^2 - 4ac) is greater than 0. If the discriminant is equal to 0, the equation has real and equal roots. And if the discriminant is less than 0, the equation has complex roots.

3. Using the Given Root:
We are given that one of the roots is 2. Let's substitute this value into the equation and solve for k.

When x = 2, the equation becomes:
2^2 - 3(2) + k = 0
4 - 6 + k = 0
-2 + k = 0
k = 2

4. Final Answer:
The value of k is 2.

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