Final answer:
To find the largest of two numbers when given their product and sum, we can use the quadratic formula. Let's denote the numbers as 'a' and 'b'. We know that 'a * b = 24' and 'a + b = 10'. We can rewrite the second equation as 'b = 10 - a' and substitute it into the first equation. Solving the quadratic equation, we find that the larger of the two numbers is 6.
Step-by-step explanation:
To find the largest of two numbers when given their product and sum, we can use the quadratic formula. Let's denote the numbers as 'a' and 'b'. We know that 'a * b = 24' and 'a + b = 10'. We can rewrite the second equation as 'b = 10 - a' and substitute it into the first equation.
Substituting 'b' into the equation 'a * b = 24', we get 'a * (10 - a) = 24'. Expanding and rearranging the equation, we have 'a^2 - 10a + 24 = 0'. Solving this quadratic equation, we find that the values of 'a' are 4 and 6. Therefore, the larger of the two numbers is 6.