Question

The trinomial x^2+bx-c has factors of (x+m)(x-n), where m,n, and b are positive. What is the relationship between the values of m and n?

Answer 1

In the given above, we have an equation that is equal to,

x² + bx - c = (x + m)(x - n)

If we are to apply distributive property on the items at the right hand side of the equation, the equation becomes,
x² + bx - c = x² - nx + mx - mn

Simplifying,
x² + bx - c = x² + (m-n)x - mn

If b is a positive number, m-n should be positive. Therefore, the value of m should be greater than the value of n in order for m-n to become positive.