Is it true that irrational roots of rational polynomial comes in pairs? How to prove this? If not give an example please.

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I have no information about this. In some places it is written true in some places it is written false. I am sure that if polynomial is quadratic then it is true. But what if not a quadratic polynomial? please help me.

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$$4x^3-3x=\frac12\iff \cos3\theta=\cos\frac\pi3$$ and there are three irrational solutions

$$\cos\frac\pi9,\cos\frac{7\pi}9,\cos\frac{15\pi}9.$$