Ta có:
\(A\left(2\right)=a.2^2+b.2+c=4a+2b+c\left(1\right)\)
\(A\left(-1\right)=a.\left(-1\right)^2+b.\left(-1\right)+c=a-b+c\left(2\right)\)
Lấy (1)+(2),ta đc:
\(A\left(2\right)+A\left(-1\right)=\left(4a+2b+c\right)+\left(a-b+c\right)=\left(4a+a\right)+\left(2b-b\right)+\left(c-c\right)\)
\(=5a+b+2c=0\)
=>\(A\left(2\right)=-A\left(-1\right)\)
=>\(A\left(2\right).A\left(-1\right)=-A\left(-1\right).A\left(-1\right)=-\left[A\left(-1\right)\right]^2\le0\) (đpcm)
A(2)=a.22+b.2+c=4a+2b+c
A(-1)=a.(-1)2+(-1).b+c=a-b+c
=> A(2) + A(-1) = 5a+b+2c=0 (theo gia thiet)
=> A(2) = -A(-1)
=> A(2).A(-1) = -A(-1).A(-1)=- <A(-1)>2 < hoac =0
Dấu = xảy ra khi a=b=c=0
