Find a monic quartic polynomial f(x) with rational coefficients whose roots include x=1-\sqrt 2 and x=2+\sqrt 5. Give your answer in expanded form.
+33652 Find a monic quartic polynomial f(x) with rational coefficients whose roots include x=1-\sqrt 2 and x=2+\sqrt 5. Give your answer in expanded form.
\((x-(1-\sqrt{2}) )(x + 1-\sqrt{2} )(x-(2+\sqrt{5} ))(x+2+\sqrt{5})\)
\((x^2 -(1-\sqrt{2})^2)(x^2 - (2+\sqrt{5})^2)\)
\(x^4 -[(1-\sqrt{2})^2+(2+\sqrt{5})^2]x^2+(1-\sqrt{2})^2(2+\sqrt{5})^2\)
Can you finish it off from there?
