A) Neither a maximum nor a minimum
B) Only one maximum
C) Only one minimum
D) Only one maximum and only one minimum
Correct Answer: C
Solution :
[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 \[0<{{a}_{0}}<{{a}_{1}}<{{a}_{2}}<.....<{{a}_{n}}.\] Here, we observe that all coefficients of different powers of x, i.e., \[{{a}_{0}},{{a}_{1}},{{a}_{2}},.....,{{a}_{n}},\] are positive. Also, only 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.You need to login to perform this action.
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