Let a and b real numbers such that x^4+2x^3-4x^2+ax+b = (Q(x))^2 for some polynomial Q(x). What is the value of a + b?
+307 Q(x)=(lx^2+mx+n)
Q(x)^2=(l^2x^2 + 2mlx^3 + (2ln+m^2)x^2+2mnx+n^2)
Therefore
l^2=1
2ml=2
ml=1
2ln+m^2=-4
a=2mn
b=n^2
If l is one, so is m.
If l is -1, so is m.
l has to be negative, because of 2ln+m^2=-4, which means 2ln is negative.
2ln=-5
n=2.5
b=6.25
a=-5
a+b=1.25
(I think)
