Question

The trinomial x2 + bx + c factors to (x + m)(x + n). If b is negative and c is positive, what must be true about m and n?

m and n are both positive.
m is positive and n is negative.
m is negative and n is positive.
m and n are both negative.

Answer 1

D) m and n should be negative

Explanation:

Answer 2

expand


`(x+m)(x+n)=x^2+mx+nx+mn`

if we compare

`1x^2+mx+nx+mn=ax^2+bx+c`

`1x^2+x(m+n)+mn=ax^2+bx+c`
a=1
b=m+n
c=mn

if b is negative and c is positive then
m+n<0 and mn>0

let's look at the 2nd one
mn>0
that means either m and n are both positive or both negative

look at the other one
m+n<0
if they are both positive, this is false
if they are both negative, this is true


therefor m and n are both negative