What are two numbers that have a sum of 12 and product of 100?

x + y =12 (1)

and xy =100 (2)

From y= 12 -x

substituting in (2) gives

x(12-x)=100

12x - x² =100

x² -12x + 100=0

discriminant = (-12)² - 4 *100

= 144 -400

=-256<0

No real solutions exist for this problem

but complex solutions are (12 + 16i)/2 and (12 - 16i)/2

= 6 + 8i and 6 -8i

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