Let a_0+a_1/2+a_2/3+...+a_n/n+1=0 , where a_i's are some real constants.

FoomyBiamy5

FoomyBiamy5

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2022-08-20

Let a 0 + a 1 2 + a 2 3 + . . . + a n n + 1 = 0 , where a i 's are some real constants.
How can we prove that the equation a 0 + a 1 x + a 2 x 2 + . . . + a n x n = 0 has at least one solution in the interval (0,1) ?

Answer & Explanation

tkaljegs

tkaljegs

Beginner2022-08-21Added 9 answers

Note that a 0 + a 1 x + a 2 x 2 + + a n x n is continuous and
0 1 ( a 0 + a 1 x + a 2 x 2 + + a n x n ) d x = 0

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