Find the value of n if both sum and product of roots of the quadratic equation mx² - 5x + n = 0 are equal to 10?

Find the value of n if both sum and product of roots of the quadratic equation mx² - 5x + n = 0 are equal to 10?

Explanation

Given the quadratic equation mx² - 5x + n = 0:

Sum of roots = -(-5/m) = 5/m

Product of roots = n/m

Given both sum and product of roots are equal to 10:

5/m = 10 => m = 1/2

n/m = 10 => n = 10m

n = 10 * (1/2)

n = 5