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Find a monic quartic polynomial with rational coefficients whose roots include x = 1 - sqrt(2) and x = 2 + sqrt(7).

 Oct 29, 2021

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(x -1-sqrt2)(x-1+sqrt2)(x-2-sqrt7)(x-2+sqrt7) =

x4 -6x3 + 4x2 +10x + 3

 Oct 29, 2021
 #1
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Best Answer

(x -1-sqrt2)(x-1+sqrt2)(x-2-sqrt7)(x-2+sqrt7) =

x4 -6x3 + 4x2 +10x + 3

Guest Oct 29, 2021
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Find a monic quartic polynomial with rational coefficients whose roots include

x = 1 - sqrt(2) and x = 2 + sqrt(7).

 

Hello Guest!

 

\(f(x)=(x-1+\sqrt{2})(x-2-\sqrt{7})\\ f(x)= x^2-\sqrt{7}\ x+\sqrt{2}\ x-3x-\sqrt{14}+\sqrt{7}-2\sqrt{2}+2\)

\(f(x)=x^2-(\sqrt{7}-\sqrt{2}+3)x-\sqrt{14}+\sqrt{7}-2\sqrt{2}+2=0\)

\(g(x)=x^2-4.2315x-1.9243\approx 0\)

laugh  !

 Oct 29, 2021

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