Maths · Relations between roots and coefficients, nature of roots
If the product of two numbers is 10 and their sum is which is the greatest of th
If the product of two numbers is 10 and their sum is \( 7, \) which is the greatest of the two numbers?
- A. -2
- B. 2
- C. 5 \)
- D. 4
Step-by-step solution
Let the two numbers be x and y. Given x+y=7 and xy=10. These are the sum and product of roots of a quadratic equation: t^2 - (sum)t + product = 0, so t^2 - 7t + 10 = 0. Factoring gives (t-2)(t-5)=0, so the numbers are 2 and 5. The greatest is 5.