Question

$Iff\left(x\right)=\{\begin{array}{cc}{x}^2-3,& 2<x<3\\ 2x+5,& 3<x<4\end{array}$, the equation whose roots are $\underset{x\to 3-}{lim}f\left(x\right)$ and $\underset{x\to 3+}{lim}f\left(x\right)is$

• A. $x^2-12x+36=0$
• B. $x^2-26x+66=0$
• C. $x^2-17x+66=0$
• D. $x^2-22x+121=0$

Answer 1

The correct option is C $x^2-17x+66=0$

$f\left(x\right)=\{\begin{array}{cc}{x}^2-3,& 2<x<3\\ 2x+5,& 3<x<4\end{array}$
$\therefore \underset{x\to 3-}{lim}f\left(x\right)=\underset{x\to 3-}{lim}(x^2-3)=6$
and $\underset{x\to 3+}{lim}f\left(x\right)=\underset{x\to 3+}{lim}(2x+5)=11$
Hence, the required equation will be
$x^2$ - (sum of roots)x + (Products of roots) = 0