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.

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if we compare


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