The number 1 radic2 is a root of a cubic polynomial t3nbsp

Question

Problem:

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.

Additional Information:

This question is basically from Mathematics as well as it is about rational coefficients and computing that the polynomial has 3 real roots and 1 root is a rational number.

Note: The solution is in handwritten format.