Question

If $2a{x}^2-\frac{x}{2}+2$ has a remainder $2$ when divided by $x-3$, then what will be the reciprocal of $a$?

• A. $1$`
• B. $12$
• C. $\frac{1}{12}$
• D. $-12$

Answer 1

Answer: (B)

$12$

Replace $x$ as $3$ in the expression:
$2a{x}^2-\frac{x}{2}+2$
$=$ $2a(3{)}^2-\frac{3}{2}+2$
$=$ $18a-\frac{3}{2}+2$
$=$ $\frac{36a+1}{2}$
So, the remainder is $\frac{36a+1}{2}$, Now substitute the value of remainder as $2$.
$\frac{36a+1}{2}$ $=2$
$36a+1=4$
$36a=3$
$a=$ $\frac{1}{12}$
The reciprocal of $a=12$.