The roots of the equation x^2 - 10x + 34 = 0 can be found by using the quadratic formula:
x = (10 +/- sqrt(10^2 - 4134)) / (2*1)
This simplifies to:
x = (10 +/- sqrt(100 - 136)) / 2
The square root of a negative number is equal to a complex number in the form a + bi, where a and b are real numbers and i is the square root of -1. Therefore, the roots of the equation x^2 - 10x + 34 = 0 are:
x = (-10 + sqrt(-36)) / 2 = (-5 + 3i) / 2 = -2.5 + 1.5i
x = (-10 - sqrt(-36)) / 2 = (-5 - 3i) / 2 = -2.5 - 1.5i
In simplest a + bi form, the roots of the equation are -2.5 + 1.5i and -2.5 - 1.5i.