Question

Given, $f\left(x\right)=2x^2+a$
If $a$ is a constant and $f\left(2\right)+f\left(3\right)=f\left(5\right)$, calculate the value of $a$.

• A. $6$
• B. $12$
• C. $24$
• D. $48$

Answer 1

The correct option is C $24$

Given, $f\left(x\right)=2x^2+a$

Also given, $f\left(2\right)+f\left(3\right)=f\left(5\right)$

$\Rightarrow f\left(2\right)=2\times (2{)}^2+a\Rightarrow 8+a$

$\Rightarrow f\left(\right(3)=2\times (3{)}^2+a\Rightarrow 18+a$

$\Rightarrow f\left(5\right)=2\times (5{)}^2+a\Rightarrow 50+a$

$\Rightarrow 8+a+18+a=50+a$

$\Rightarrow 2a-a=50-26$

$\Rightarrow a=24$