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?

Question

Chaya

Mathematics

1 September, 05:02

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?

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Thompson · 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.