The sum of two numbers is 25 and their product is 156. Find the smaller number.
Answer: A
Let the numbers be x and y. x + y = 25 and xy = 156.
We can form a quadratic equation: \(t^2 - (sum)t + (product) = 0\).
\(t^2 - 25t + 156 = 0\).
We need to find two numbers that multiply to 156 and add up to 25. These are 12 and 13.
\((t-12)(t-13) = 0\).
The numbers are 12 and 13. The smaller number is 12.