Find the polynomial of minimal degree, in x which has rational coefficients, leading coefficient 1, and roots 1+rt2 and 1+rt3 (Write the terms in decreasing order of degree.)
1 + rt2 is a root => 1 - rt 2 is also a root
1 + rt3 is a root => 1 - rt 3 is also a root
P(x) = \(((x-1)^2 - 2)((x-1)^2 - 3) \)
P(x) = \((x-1)^4 - 5(x-1)^2 + 6\)
P(x) = \(x^4-4x^3+6x^2-4x+1-5x^2+10x-5+6\)
P(x) = \(x^4-4x^3+x^2+6x+2\)
