P(x)={{a}_{0}}+{{a}_{1}}{{x}^{2}}+{{a}_{2}}{{x}^{4}}+....+{{a}_{n}}{{x}^{2n}},x\in R\] and \[0<{{a}_{0}}<{{a}_{1}}<{{a}_{2}}<..... all="" also="" are="" coefficients="" different="" here="" i.e.="" observe="" of="" only="" positive.="" powers="" that="" we="" x="">EVEN powers of x are involved. THEREFORE, P(x) cannot have any maximum value. Moreover, P(x) is minimum, when x = 0, i.e., \[{{a}_{0}}.\] Therefore, P(x) has only one minimum.

"> P(x)={{a}_{0}}+{{a}_{1}}{{x}^{2}}+{{a}_{2}}{{x}^{4}}+....+{{a}_{n}}{{x}^{2n}},x\in R\] and \[0<{{a}_{0}}<{{a}_{1}}<{{a}_{2}}<..... all="" also="" are="" coefficients="" different="" here="" i.e.="" observe="" of="" only="" positive.="" powers="" that="" we="" x="">EVEN powers of x are involved. THEREFORE, P(x) cannot have any maximum value. Moreover, P(x) is minimum, when x = 0, i.e., \[{{a}_{0}}.\] Therefore, P(x) has only one minimum.

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Let \[P(x)={{a}_{0}}+{{a}_{1}}{{x}^{2}}+{{a}_{2}}{{x}^{4}}+.....+{{a}_{n}}{{x}^{2n}}\] be a polynomial in a real variable x with\[0<{{a}_{0}}<{{a}_{1}}<{{a}_{2}}<....<{{a}_{n}}\]. The function P(x) has

Joint Entrance Exam - Main (JEE Main) Mathematics in Joint Entrance Exam - Main (JEE Main) . 11 months ago

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[c] The given polynomial is \[P(x)={{a}_{0}}+{{a}_{1}}{{x}^{2}}+{{a}_{2}}{{x}^{4}}+....+{{a}_{n}}{{x}^{2n}},x\in R\] and \[0<{{a}_{0}}<{{a}_{1}}<{{a}_{2}}<..... all="" also="" are="" coefficients="" different="" here="" i.e.="" observe="" of="" only="" positive.="" powers="" that="" we="" x="">EVEN powers of x are involved. THEREFORE, P(x) cannot have any maximum value. Moreover, P(x) is minimum, when x = 0, i.e., \[{{a}_{0}}.\] Therefore, P(x) has only one minimum.

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Posted on 05 Aug 2024, this text provides information on Joint Entrance Exam - Main (JEE Main) related to Mathematics in Joint Entrance Exam - Main (JEE Main). Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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