Question

If x2 + mx + m is a perfect-square trinomial, which equation must be true?

x2 + mx + m = (x – 1)2
x2 + mx + m = (x + 1)2
x2 + mx + m = (x + 2)2
x2 + mx + m = (x + 4)2

Answer 1

for
`1x^2+bx+c` to be a perfect square trinomial,
`c=((b)/(2))^2`

or
`x^2+mx+m`

thereore,
`m=((m)/(2))^2`

`m=(m^2)/(4)`

4m=m²

m²-4m=0

(m)(m-4)=0

m=0 and m-4=0

m=0 and m=4

so you could have

x²+0x+0=(x-0)²

or

x²+4x+4=(x+2)²

answer is 3rd optio, (x+2)²