Consider all possible polynomials P(x)=a0+a1x+a2x2+........+a10x10 with real coefficients satisfying |P(x)|≤|x| for all x∈[−1,1]. Then the maximum possible value of (2a0+3a1)10is

|P(0)|≤0 ⇒a0=0 Now, |a1x+a2x2+.....|≤|x| |a1+a2x+.....|≤ 1 so, |a1|≤ 1.

Consider all possible polynomials P(x)=a0+a1x+a2x2+........+a10x10 with real coefficients satisfying |P(x)|≤|x| for all x∈[−1,1]. Then the maximum possible value of (2a0+3a1)10is

|P(0)|≤0 ⇒a0=0 Now, |a1x+a2x2+.....|≤|x| |a1+a2x+.....|≤ 1 so, |a1|≤ 1.

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Consider all possible polynomials $P (x) = a_{0} + a_{1} x + a_{2} x^{2} + ........ + a_{10} x^{10}$ with real coefficients satisfying $| P (x) | \leq | x |$ for all $x \in [- 1, 1] .$ Then the maximum possible value of ${(2 a_{0} + 3 a_{1})}^{10}$ is

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$2^{10}$

$3^{10}$

$5^{10}$

$1$

answer is B.

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$| P (0) | \leq 0 \Rightarrow a_{0} = 0 N o w, | a_{1} x + a_{2} x^{2} + ..... | \leq | x | | a_{1} + a_{2} x + ..... | \leq 1 s o, | a_{1} | \leq 1.$

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Consider all possible polynomials P(x)=a0+a1x+a2x2+........+a10x10 with real coefficients satisfying |P(x)|≤|x| for all x∈[−1,1]. Then the maximum possible value of (2a0+3a1)10is

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Consider all possible polynomials $P (x) = a_{0} + a_{1} x + a_{2} x^{2} + ........ + a_{10} x^{10}$ with real coefficients satisfying $| P (x) | \leq | x |$ for all $x \in [- 1, 1] .$ Then the maximum possible value of ${(2 a_{0} + 3 a_{1})}^{10}$ is