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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.)

 Apr 19, 2019
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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) = \(x^4-4x^3+x^2+6x+2\)

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 Apr 21, 2019

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