Answer by Deif for Advanced Calculus Homework
As you said, $0=a_1/2+a_2/3+\ldots+a_n/(n+1)=\int_0^1p(x)dx$. If there was no $x$ in $]0,1[$ such that $p(x)=0$ then $p(x)$ would be positive in all the interval $]0,1[$ or negative in all $]0,1[$...
View ArticleAdvanced Calculus Homework
For real numbers $a_1, a_2, \dots , a_n$, let $p(x)= a_1 x + a_2x^2 + \dots + a_nx^n$ for all $x \in \mathbb{R}$. Suppose that $$\frac{a_1}{2} + \frac{a_2}{3} + \dots + \frac{a_n}{n+1} = 0.$$ Prove...
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