If the arithmetic mean of two numbers is 25 and their geometric mean is 24, then an equation with the given numbers as its roots, is

Name: If the arithmetic mean of two numbers is 25 and their geometric mean is 24, then an equation with the given numbers as its roots, is
Uploaded: 2026-08-31T17:54:14.960759+05:30
Duration: 55 s
Description: If the arithmetic mean of two numbers is 25 and their geometric mean is 24, then an equation with the given numbers as its roots, is

Solution

The arithmetic mean 25 gives a sum of $$50$$ and the geometric mean 24 gives a product of $$24^2 = 576$$. A quadratic with these roots is $$x^2 - (\text{sum})x + (\text{product}) = 0$$. Hence the equation is $$x^2 - 50x + 576 = 0$$.