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.
+33657 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−√2))(x+1−√2)(x−(2+√5))(x+2+√5)
(x2−(1−√2)2)(x2−(2+√5)2)
x4−[(1−√2)2+(2+√5)2]x2+(1−√2)2(2+√5)2
Can you finish it off from there?
