Find a monic quartic polynomial f(x) with rational coefficients whose roots include 1 - sqrt2 and 2 + sqrt5 . Give your answer in expanded form.
The four roots of this quartic are: 1 - sqrt(2) 1 + sqrt(2) 2 + sqrt(5) 2 - sqrt(5)
The polynomial will be:
[ x - ( 1 - sqrt(2) ) ] · [ x - ( 1 + sqrt(2) ) ] · [ x - ( 2 + sqrt(5) ] · [ x - ( 2 - sqrt(5) ) ] = 0
You'll need to multiply it out ...
