To find two numbers that multiply to 120 and add to 2, we can use algebra. Let's call the two numbers x and y, so we have:
x + y = 2 (equation 1)
xy = 120 (equation 2)
We can solve equation 1 for one of the variables, say y:
y = 2 - x
Now we can substitute this expression for y into equation 2:
x(2 - x) = 120
Expanding the left side, we get:
2x - x^2 = 120
Rearranging and simplifying:
x^2 - 2x + 120 = 0
Now we can use the quadratic formula to solve for x:
x = [2 ± sqrt(2^2 - 4(1)(120))] / 2
x = [2 ± sqrt(-472)] / 2
Since the square root of a negative number is not a real number, this equation has no real solutions. Therefore, there are no two real numbers that multiply to 120 and add to 2.