Problem #PRU-65704

Problems Methods Mathematical induction Mathematical induction (other) Calculus Number sequences Number sequences (other)

14–15 4.0

Problem

Author: G. Zhukov

The square trinomial $f (x) = a x^{2} + b x + c$ that does not have roots is such that the coefficient $b$ is rational, and among the numbers $c$ and $f (c)$ there is exactly one irrational.

Can the discriminant of the trinomial $f (x)$ be rational?

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