Answer:
To find the coordinates of the root of the equation y = 3 + 2x - x^2, we need to find the values of x where y = 0 (because the root is the point where the function intersects the x-axis). So we can set y equal to 0 and solve for x:
0 = 3 + 2x - x^2
Rearranging, we get:
x^2 - 2x - 3 = 0
We can factor the quadratic equation by finding two numbers that add up to -2 and multiply to -3. These numbers are -3 and 1, so we can write:
(x - 3)(x + 1) = 0
This equation is true when either x - 3 = 0 or x + 1 = 0. So the roots of the equation are:
x = 3 or x = -1
Therefore, the coordinates of the roots of the equation y = 3 + 2x - x^2 are (3, 0) and (-1, 0).