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  • Consider the function <img alt="f(x)=\left\{\begin{array}{cc} \frac{p(x)}{x-2} ; &amp

Consider the function f(x)=\left\{\begin{array}{cc} \frac{p(x)}{x-2} ; & x \neq 2 \\ 7 ; & x=2 \end{array}\right. where P(x) is a polynomial such that \mathrm{p}^{\prime \prime \prime}(\mathrm{x}) is identically equal to 0 and \mathrm{p}(3)=9  If f(x) is continuous at x = 2, then p(x) is

 

Option: 1

2 x^2+x+6


Option: 2

2 x^2-x-6


Option: 3

x^2+3


Option: 4

x^2-x+7


Answers (1)

best_answer

Since \mathrm{P}^{\prime \prime \prime}(\mathrm{x})=0

Let p(x)=a x^2+b x+c \hspace{1cm} \begin{aligned} & \mathrm{p}(2)=0 \\ & 4 a+2 b+c=0 \\ & 9 a+3 b+c=9 \\ & p^{\prime}(2)=7 \\ & \Rightarrow 4 a+b=7 \end{aligned}

Solve 1,2 and 3 to get a,b,c

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Riya

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