Final answer:
The least number of vertices a graph with 50 edges can have is 10.
Step-by-step explanation:
In a graph, the number of edges (E) is related to the number of vertices (V) by the formula E = V*(V-1)/2. By rearranging the formula, we can solve for V. Since we are given that the graph has 50 edges, we can substitute E = 50 into the formula:
50 = V*(V-1)/2
Now, we can solve this equation to find the least number of vertices. We can start by multiplying both sides of the equation by 2:
100 = V*(V-1)
Next, we can expand the right side of the equation:
100 = V^2 - V
Now, we can rearrange the equation to solve for V:
V^2 - V - 100 = 0
We can solve this quadratic equation using factoring, completing the square, or the quadratic formula. By factoring, we find:
(V - 10)(V + 10) = 0
This means that V - 10 = 0 or V + 10 = 0. So, the possible values for V are 10 and -10. However, in the context of the problem, the number of vertices cannot be negative. Therefore, the least number of vertices the graph can have is 10.