AP EAMCET · Maths · Differentiation
If \(\frac{d}{d x}\left(\frac{1+x^2+x^4}{1+x+x^2}\right)=a x+b\) then \((a, b)=\)
- A \((-1,2)\)
- B \((-2,1)\)
- C \((2,-1)\)
- D \((1,2)\)
Answer & Solution
Correct Answer
(C) \((2,-1)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { } \frac{1+x^2+x^4}{1+x+x^2}=\frac{\left(1+x+x^2\right)\left(1-x+x^2\right)}{1+x+x^2}=x^2-x+1 \\ & \frac{d}{d x}\left(\frac{1+x^2+x^4}{1+x+x^2}\right)=2 x-1 \Rightarrow a=2, b=-1\end{aligned}\)
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