Mathematics, 27.06.2019 03:00 angelequej1167
If (2-square root of 3 ) is a root of a polynomial with integer coefficients which of the follow must be another root a. square root of 3-2 b.3-square root of 2 c.2 + square root of 3 d.2 -square root of 3
Answers: 1
![(2-\sqrt3)-a\ root\ of\ a\ polynomial\\\\another\ root\ must\ be\ C.\ (2+\sqrt3),\ because\\\\\ [x-(2-\sqrt3)][x-(2+\sqrt3)]=(x-2+\sqrt3)(x-2-\sqrt3)\\\\=[(x-2)+\sqrt3][(x-2)-\sqrt3]\\\\\text{use}\ (a-b)(a+b)=a^2-b^2\\\\=(x-2)^2-(\sqrt3)^2\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=x^2-2(x)(2)+2^2-3=x^2-4x+4-3=x^2-4x+1](/tpl/images/0021/7973/e6ade.png)
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If (2-square root of 3 ) is a root of a polynomial with integer coefficients which of the follow mus...
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