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- Feb 14, 2012
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Let $p$, $q$ and $r$ be roots of polynomial \(\displaystyle x^3-9x+9=0\). Show that \(\displaystyle p^2+p-6\) is equal to $q$ or $r$.
It is sufficient to show that \(\displaystyle p^2+p-6\) is a root of \(\displaystyle x^3-9x+9\) different from $p$. We may as well also note that \(\displaystyle x^3-9x+9\) has three distinct real roots.Let $p$, $q$ and $r$ be roots of polynomial \(\displaystyle x^3-9x+9=0\). Show that \(\displaystyle p^2+p-6\) is equal to $q$ or $r$.