The discussion focuses on finding a polynomial with integer coefficients for which the complex number \(\sqrt{2} + i\) is a zero. The proposed solution involves expanding the expression \((\sqrt{2} + i)^2\) and \((\sqrt{2} + i)^4\) to derive the polynomial. The initial attempt yielded the expression \(x^2 - 2\sqrt{2}x + 2 - i\), which is not a valid polynomial with integer coefficients due to the presence of \(\sqrt{2}\) and \(i\). The correct approach requires ensuring that all coefficients are integers.
PREREQUISITESMathematics students, educators, and anyone interested in algebraic structures involving complex numbers and polynomial equations.
duki said:Homework Statement
Find a polynomial with integer coefficient for which \sqrt(2) + i is a zero.
Homework Equations
The Attempt at a Solution
I'm not sure where to really start with this one. It is on my review sheet, and I can't remember how to do it. Could someone give me a hand?