Let \( f(x)=a x^{2}+b x+c ; a, b, c \in R \) It is given \( |f(x)| \leq 1, \forall|x| \leq 1 \).....

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Let \( f(x)=a x^{2}+b x+c ; a, b, c \in R \)
\( \mathrm{P} \)
It is given \( |f(x)| \leq 1, \forall|x| \leq 1 \).
W.
Now, answer the following questions.
The possible maximum value of \( \frac{8}{3} a^{2}+2 b^{2} \) is given by
(1) 32
(2) \( \frac{32}{3} \)
(3) \( \frac{2}{3} \)
(4) \( \frac{16}{3} \)


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