Question

Let $f\left(x\right)=5a^2+4(x-1)-x^2$,$xϵR$ and $a$ is a real constant. If the maximum value of $f\left(x\right)$ is $20$ then $a$ is

• A. $-2$
• B. $4$
• C. $2$
• D. none of these

Answer 1

Answer: (A), (C)

$-2$
$2$

$f\left(x\right)=5a^2+4(x-1)-x^2=5a^2-(x^2-4x+4)=5a^2-(x-2{)}^2$
maximum value of $f\left(x\right)=5a^2=20$ (given)
$\Rightarrow a^2=4\Rightarrow a=\pm 2$