If f(x) is a polynomial of degree three with leading coefficient 1 and $f(1)=1$, $f(2)=4$, $f(3)=9$ then prove $f(x)=0$ has a root in interval $(0,1)$

score 146 · Answer 15 · 2026-04-15 06:03:43

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Show that $\sum\limits_{k=1}^{n-1} (n-k) x^k$ is non-decreasing for $x \in ]-1,1[$.

Published on 15 Apr 2026 - 6:03

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If f(x) is a polynomial of degree three with leading coefficient 1 and $f(1)=1$, $f(2)=4$, $f(3)=9$ then prove $f(x)=0$ has a root in interval $(0,1)$

Show that $\sum\limits_{k=1}^{n-1} (n-k) x^k$ is non-decreasing for $x \in ]-1,1[$.

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