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> Prove that if $c > 1$ then the polynomial $$p(x) = x^{4} - 2cx^{2} + x + c^{2} - c$$ has a real root, and if $c < \frac{3}{4}$ it has no real roots.
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* For the first part, it suffices to find a point $a$ such that $p(a) \leqslant 0$ since $p(0) = c^{2} - c > 0$, but I don't know what such point is.
* For the second part, my idea is to use proof by contradiction but I don't know how to proceed.

Can you give me some hints? Thanks.