Given x = 1 is a root of the equation x² + kx + 3 = 0 it means it satisfies the equation.

Substituting x = 1 in equation -

1² + k(1) + 3 = 0

Putting the value of k in the given equation : x² + kx + 3 = 0

This reduced to the quadratic equation x² - 4x + 3 = 0

Using the splitting middle term - the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation

= 1.3

= 3

And either of their sum or difference = b

= - 4

Thus the two terms are - 1 and - 3

Sum = - 1 - 3 = - 4

Product = - 1. - 3 = 3

x(x-1)-3(x-1) = 0

(x-1)(x-3) = 0

x = 1 or x = 3

Thus other root is 3.