Question

If $a$ and $b$ are two integers such that $10a+b=20$ and $g\left(x\right)=x^2+ax+b$. Then, integer n such that $g\left(10\right).g\left(11\right)=g\left(n\right)$ is

• A. $15$
• B. $65$
• C. $130$
• D. $165$

Answer 1

The correct option is C

$130$

Explanation for the correct option:

Step 1. Find the value of integer $n$:

Given that, $g\left(x\right)=x^2+ax+b$

and $g\left(10\right)g\left(11\right)=g\left(n\right)$

$(100+10a+b)(121+11a+b)=n^2+an+b$

$(100+20)(121+10a+b+a)=n^2+an+20–10a$

$\left(120\right)(141+a)=(n^2+20)+a(n–10)$

$120\times 141+120a=(n^2+20)+(n–10)a$

Step 2. compare the variable part of the equation:

$n–10=120$

$\mathbf{\therefore }\mathit{n}\mathbf{}\mathbf{=}\mathbf{}\mathbf{130}$

Hence, Option ‘C’ is Correct.