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?

Answer 1

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

Answer 2

Answer:

D) m and n should be negative

Step-by-step explanation: