Calculation Of Rational Coefficients

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Question

The number 1 + √2 is a root of a cubic polynomial t³ + at² + bt + c with rational coefficients. Prove that this polynomial has three real roots and one root is a rational number.

Summary

The question belongs to Mathematics and it is about rational coefficients and calculating that the polynomial has 3 real roots and 1 root is a rational number.

Note: The solution is in handwritten format.

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