Question

The trinomial x2+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? Explain

Answer 1

(m - n ) = b

mn = c

The relationship between m and n is such that their product is c and their difference is b

Explanation:

roots are x = -m and x = n

-m = -b/2 - root(b*b + 4c)/2

n = -b/2 + root(b*b + 4c)/2

(x + m)(x -n) = x*x +(m - n)x - mn

(m - n ) = b

mn = c

Answer 2

Sample Answer: The value of m must be greater than the value of n. When you multiply the binomials, the middle term is the result of combining the outside and inside products. So, bx = –nx + mx, or bx = (–n + m)x. This means that b = –n + m. When adding numbers with opposite signs, you subtract their absolute values, and keep the sign of the number having the larger absolute value. Since b is positive, m must have the larger absolute value.

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