Question

Cho : f(x) = ax² + bx + c biết 5a+2b= -2c . Cm : f(2).f(-1) \(\le\) 0

Answer 1

Hình như đề sai nha bạn phải là 5a+b=-2c mới đúng

Có \(5a+b=-2c\Rightarrow5a+b+2c=0\)

\(f\left(x\right)=ax^2+bc+c\)

\(\Rightarrow f\left(-1\right)=a.\left(-1\right)+b.\left(-1\right)+c=a-b+c\)

\(\Rightarrow f\left(2\right)=a.2^2+b.2+c=4a+2b+c\)

\(\Rightarrow f\left(-1\right)+f\left(2\right)=a-b+c+4a+2b+c=5a+b+2c=0\)

\(\Rightarrow f\left(-1\right)+f\left(2\right)=0\Rightarrow f\left(-1\right)=-f\left(2\right)\)

Xét \(f\left(-1\right).f\left(2\right)=[-f\left(2\right)].f\left(2\right)=-[f\left(2\right)]^2\le0\)

Vậy \(f\left(-1\right).f\left(2\right)\le0\)