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  • Choose the correct answer out of 4 options given against each Question Let f(x)= x^{2}-1,0<x<2 \\ 2 x+3,2 <= x<3 the quad ratic equation whose roots are \lim _{x \rightarrow 2} f(x) \text { and } \lim _{x \rightarrow 2} f(x) isA. x2 – 6x + 9 = 0

Choose the correct answer out of 4 options given against each Question

Let f(x)=\begin{array}{l} x^{2}-1,0<x<2 \\ 2 x+3,2 \leq x<3 \end{array}  the quadratic equation whose roots are 

\lim _{x \rightarrow 2} f(x) \text { and } \lim _{x \rightarrow 2} f(x)  is

\\A. x\textsuperscript{2} - 6x + 9 = 0\\ B. x\textsuperscript{2} -7x + 8 = 0\\ C. x\textsuperscript{2} - 14x + 49 = 0\\ D. x\textsuperscript{2} - 10x + 21 = 0 \\

Answers (1)

\\ LHL=\mathop{\lim }_{x \rightarrow \mathop{2}^{-}}f \left( x \right) =\mathop{\lim }_{x \rightarrow \mathop{2}^{-}} \left( x^{2}-1 \right) =3 \\ \\ RHL=\mathop{\lim }_{x \rightarrow \mathop{2}^{+}}f \left( x \right) =\mathop{\lim }_{x \rightarrow \mathop{2}^{+}} \left( 2x+3 \right) =7 \\ \\ \text{The quadratic equation whose roots are 3 and 7 are } \left( x-3 \right) \left( x-7 \right)\\ =x^{2}-10x+21 \\ \\

Hence, the answer is option D

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